Acc. Sc. Torino Atti Sc. Fis. 149 (2015), 17-34

Size: px
Start display at page:

Download "Acc. Sc. Torino Atti Sc. Fis. 149 (2015), 17-34"

Transcription

1 Acc. Sc. Torino Atti Sc. Fis. 149 (2015), 17-34

2 Commemorazioni di Accademici in unità h/2 pi greco stesse unità

3 Commemorazioni di Accademici f(e, cos theta) l+1/2 i poli di Regge Potential Scattering

4 Commemorazioni di Accademici

5 Commemorazioni di Accademici Kennedy was shot

6 Commemorazioni di Accademici progresso a rischio zero

7 Commemorazioni di Accademici Dialogo AutobiograÞ a

8 Commemorazioni di Accademici

9 Commemorazioni di Accademici Scattering Problems with Spin Orbit Coupling Tensor Force and Intermediate Coupling in P Shell Nuclei On the Polarization of High Energy Nucleons Scattered by a Nuclear Field Pion Production for Polarized Protons Reaction P+P---> pi+d with Polarized Protons Remarks on the Anti Proton inspirehep.net Þ nd a regge, t

10 Commemorazioni di Accademici Angular Correlations between Decay Planes of Tau-Mesons and their Production Geometry Stability of a Schwarzschild Singularity The properties of Spin 2 Particles Additional Remarks and Errata Corrige to a Paper on the Theory of Spin 2 Gravitational Fields and Quantum Mechanics Analytic Properties of the Scattering Matrix On the Analytic Behaviour of the Eigenvalues of the S Matrix in the Complex Plane of the Energy Construction of Potentials from Resonance Parameters Symmetry Properties of Clebsch-Gordan Coefficients Symmetry Properties of Racah s Coefficients Introduction to Complex Orbital Momenta Bound States, Shadow States and Mandelstam Representation General Relativity without Coordinates A Discussion of the Noyes and Wong Equation for Potential Scattering Lectures on complex energy and angular momentum in potential scattering Potential Scattering for Complex Energy and Angular Momentum High Energy Limit of Scattering Amplitudes Maximum Analiticity Principle in Angular Momentum Interpolation Problem in Theory of Complex Angular Momentum, Dynamical Equation for the Jost Function On Properties of Landau Curves Dynamical Equations and Angular Momentum

11 Commemorazioni di Accademici Potential Scattering Differential Properties of Feynman Amplitudes Semiclassical Limit of Racah Coefficients A Geometrical Model showing independence of Locality Positivity of Energy Algebraic Topology Methods in Theory of Feynman Relativstic Amplitudes he fundamental Group of Poincare and Analytic Properties of Feynman Amplitudes, Nobel Symp Elem Part Theory The Monodromy Rings of a Class of Self-energy Graphs The Monodromy Rings of One Loop Feynman Integrals Phonon Excitations in Liquid He II The Monodromy Rings of the Necklace Graphs Veneziano Amplitudes, Angular Momentum Coefficients and Relativistic Symmetries Rotational Motion at Large Angular Momentum in even-even Deformed Nuclei Perturbation on the Mixmaster Universe On the Back-Bending in the Rotational Motion General Relativity a` la String: A Progress Report Band Hybridization in Rotational Motion Veneziano Amplitudes, Angular Momentum Coefficients and Related Symmetries Feynman Integrals Magic without Magic The Relativistic Spherical Top

12 Commemorazioni di Accademici Role of Surface Integrals in the Hamiltonian Formulation of General Relativity Vortices in He II, Current Algebras and Quantum Knots On the Density Oscillations in Finite Systems Geometrical Formulation of SuperGravity as a Theory on a Supergroup Manifold Unified Approach to Strings and Vortices with Soliton Solutions On the Density Oscillations in Finite Systems Constrained Hamiltonian Systems Conformal Properties of a Class of Exac Solv N Body Problems in Space Dimension 1 General Relativity a la String: a progress report Statistical Mechanics Models and the Modular Group On the Density Oscillations in Finite Systems Old Problems and New Hopes in S Matrix Theory Ising and Dimer Models on the Lobachevsky Plane General Relativity à la String: a Progress Report Gravity and SuperGravity as Gauge Theories on a Group Manifold Gauge Theory of Gravity and SuperGravity on a Group Manifold Torsion and Quantum Gravity Ghost Fields, BRS and Extended SuperGravity as Application of Gauge Geometry

13 Commemorazioni di Accademici auge Theories of SuperGravity on Orthosymplectic Supergroup Manifolds The Gauge Group and Geometry of SuperGravity Geometrical Formulation of SuperGravity Theories on Orthosymplectic Supergroup Manifolds Gauge Theories of SuperGravity on Orthosymplectic Supergroup Manifolds Gauge Fields as Phonon Exitations in a Condensate of Dual Strings A General Scheme for Bidimensional Models with Associate Linear Sets Geometrical Formulation of Supergravity Theories on Orthosymplectic Supergroup Manifold Group Theory Construction of 2d Models with Infinite Set of Conservation Laws Graded Lie Algebra Cohomology and Supergravity Geometric Formulation of SuperGravity as a Theory on a Super Group Manifold Gauge Theories of Unification Coupling of Matter to Sgravity Fields from the Rheonomic Simmetry Point of View and Origin of the Auxiliary Fields Unified Gravity Theories SuperGravity and Cohomology Theory: Progress and Problems in 5 Dimensions Group Manifold Approach to SuperGravity and Coupling of Matter Fields Graded Lie Algebra Cohomology and SuperGravity Coupling of Matter to Sgravity from Rheonomic Symmetry Point of View and the Origin of the Aux Fields

14 Commemorazioni di Accademici Gauge Theories of Unification Dimer Covering and Ising Model on Lattice Homogeneous under Icosaedr Gr SuperGroup Manifold Formulation of Wess- Zumino Multiplet Revisited: the Super Current and the SuperGravity Auxiliary Fields Group Manifold Approach to Gravity and SGravity Geometrical 1st Order SGravity in 5 Space-time Dimensions Group Manifold Approach in Unified Gravity Theories Approccio geometrico alla Supergravità ed unificazione delle interazioni Recent Developments in the Group Manifold Approach Group Manifold Approach and D=1 Super Gravity Unified Gravity Theories Gravity Theories with Asymptotic Flat Instantons A New Group Theoretical Technique for the Analysis of Bianchi Identities Recent Developments in the Group Manifold Approach Consistent SuperGravity in 6 D without Action Invariance Quantum Vortices An Elementary Course on General Relativitty The Group Manifold Approach to Unified Gravity Group Manifold Approach and D=11 SGravity Quantum Vortices and Diff(R3)

15 Commemorazioni di Accademici Gravity on a Lattice A Science Fiction Scenario Unified Gravity Theories Covariant Canonical Formalism for the Group Manifold Covariant Canonical Formalism for Gravity and Supergravity The Group Manifold Hamiltonian for SuperGravity Covariant Canonical Formalism for SuperGravity Exterior Canonical Formalism for Unified Gravity Covariant Canonical Formalism for Gravity Theories An Elementary Course on General Relativity Covariant Canonical Formalism for Gravity and SuperGravity Lie Groups and Gravity Theory On Broken Symmetries and Gravity Comments on the Canonical Formalism for General Relativity The Group Structure of SuperGravity Covariant Canonical Formalism for Gravity On Broken Symmetries and Gravity An elementary course on General Relativity (in Spanish) Discrete Yang Mills Theories Lorentz Invariance and the Group Manifold Covariant Canonical Formalism for Polynomial S-Gravity in any Dimension On Strings and JDouglas Variational Principle

16 Commemorazioni di Accademici Lorentz Invariance and the Group Manifold Canonical Theories from the Group Manifold Lorentz Invariance in Tangent Space Normal Coordinates in Canonical Formalism Group Manifold Derivation of Canonical Theories The Supergroup Manifold Formulation of the Wess-Zumino Multiplet Revisited: SuperCurrent and SuperGravity Auxiliary Fields Canonical 2+1-d Quantum Gravity Group Manifold Derivation of Canonical Theories Canonical Normal Coordinates Homotopy Groups and 2+1-D Quantum Gravity Homotopy Groups ad 2+1-D Quantum de Sitter Gravity SU(2)-q and 2+1 Quantum Gravity 2+1 Q Gravity up to 2 Handles 2+1-dimensional Quantum Gravity 2+1 Quantum Gravity (2+1) gravity for genus >=1 2+1 Quantum Gravity The mapping class group for genus D Quantum Gravity for High Genus The Mapping Class Group for Genus 2

17 Commemorazioni di Accademici 2+1 Quantum Gravity for High Genus Quantum Gravity and Quantum Groups Quantization of 2+1 gravity for genus 2 Quantum Gravity and Quantum Groups Picard Fuchs Equations Mirror Symmetry II Duality Group for Calabi Yau 2-moduli Space Invariants of 2+1 Gravity Quantization of 2+1 Gravity nvariants of 2+1 Quantum Gravity A Search for Non Perturbative Dualities of Local N=2 Yang- Mills Theories from Calabi Yau 3-folds Exact Solutions of the Ising Model on Group Lattices of Genus g >= 1 Word Problem and Decimation Procedure in the Ising Model on Infinite The Swiss Cheese Hypothesis Combinatorial and Topological Approach to the 3D Ising Model Discrete Structures in Gravity Extension of Geodesic Algebras to Continuouus Genus Some Thoughts on the Future of Unified Models

18 Commemorazioni di Accademici L infinito cercare L Universo senza fine La relatività di Einstein Infinito Dialogo Addendum

Pietro Fre' SISSA-Trieste. Paolo Soriani University degli Studi di Milano. From Calabi-Yau manifolds to topological field theories

Pietro Fre' SISSA-Trieste. Paolo Soriani University degli Studi di Milano. From Calabi-Yau manifolds to topological field theories From Calabi-Yau manifolds to topological field theories Pietro Fre' SISSA-Trieste Paolo Soriani University degli Studi di Milano World Scientific Singapore New Jersey London Hong Kong CONTENTS 1 AN INTRODUCTION

More information

String Theory in a Nutshell. Elias Kiritsis

String Theory in a Nutshell. Elias Kiritsis String Theory in a Nutshell Elias Kiritsis P R I N C E T O N U N I V E R S I T Y P R E S S P R I N C E T O N A N D O X F O R D Contents Preface Abbreviations xv xvii Introduction 1 1.1 Prehistory 1 1.2

More information

Chern-Simons Theory and Its Applications. The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee

Chern-Simons Theory and Its Applications. The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee Chern-Simons Theory and Its Applications The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee Maxwell Theory Maxwell Theory: Gauge Transformation and Invariance Gauss Law Charge Degrees of

More information

Geometry and Physics. Amer Iqbal. March 4, 2010

Geometry and Physics. Amer Iqbal. March 4, 2010 March 4, 2010 Many uses of Mathematics in Physics The language of the physical world is mathematics. Quantitative understanding of the world around us requires the precise language of mathematics. Symmetries

More information

Quantum Field Theory. and the Standard Model. !H Cambridge UNIVERSITY PRESS MATTHEW D. SCHWARTZ. Harvard University

Quantum Field Theory. and the Standard Model. !H Cambridge UNIVERSITY PRESS MATTHEW D. SCHWARTZ. Harvard University Quantum Field Theory and the Standard Model MATTHEW D. Harvard University SCHWARTZ!H Cambridge UNIVERSITY PRESS t Contents v Preface page xv Part I Field theory 1 1 Microscopic theory of radiation 3 1.1

More information

Modern Geometric Structures and Fields

Modern Geometric Structures and Fields Modern Geometric Structures and Fields S. P. Novikov I.A.TaJmanov Translated by Dmitry Chibisov Graduate Studies in Mathematics Volume 71 American Mathematical Society Providence, Rhode Island Preface

More information

QUANTUM MECHANIC S. Symmetries

QUANTUM MECHANIC S. Symmetries Walter Greiner Berndt Müller QUANTUM MECHANIC S Symmetries 1. Symmetries in Quantum Mechanics 1 1.1 Symmetries in Classical Physics 1 1.2 Spatial Translations in Quantum Mechanics 1 9 1.3 The Unitary

More information

Particles and Strings Probing the Structure of Matter and Space-Time

Particles and Strings Probing the Structure of Matter and Space-Time Particles and Strings Probing the Structure of Matter and Space-Time University Hamburg DPG-Jahrestagung, Berlin, March 2005 2 Physics in the 20 th century Quantum Theory (QT) Planck, Bohr, Heisenberg,...

More information

Quantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals

Quantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals Kerson Huang Quantum Field Theory From Operators to Path Integrals Second, Revised, and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA I vh Contents Preface XIII 1 Introducing Quantum Fields

More information

QUANTUM FIELD THEORY. A Modern Introduction MICHIO KAKU. Department of Physics City College of the City University of New York

QUANTUM FIELD THEORY. A Modern Introduction MICHIO KAKU. Department of Physics City College of the City University of New York QUANTUM FIELD THEORY A Modern Introduction MICHIO KAKU Department of Physics City College of the City University of New York New York Oxford OXFORD UNIVERSITY PRESS 1993 Contents Quantum Fields and Renormalization

More information

Twistors, amplitudes and gravity

Twistors, amplitudes and gravity Twistors, amplitudes and gravity From twistor strings to quantum gravity? L.J.Mason The Mathematical Institute, Oxford lmason@maths.ox.ac.uk LQG, Zakopane 4/3/2010 Based on JHEP10(2005)009 (hep-th/0507269),

More information

Quantum Mechanics: Fundamentals

Quantum Mechanics: Fundamentals Kurt Gottfried Tung-Mow Yan Quantum Mechanics: Fundamentals Second Edition With 75 Figures Springer Preface vii Fundamental Concepts 1 1.1 Complementarity and Uncertainty 1 (a) Complementarity 2 (b) The

More information

Contents. Preface to the First Edition Preface to the Second Edition

Contents. Preface to the First Edition Preface to the Second Edition Contents Preface to the First Edition Preface to the Second Edition Notes xiii xv xvii 1 Basic Concepts 1 1.1 History 1 1.1.1 The Origins of Nuclear Physics 1 1.1.2 The Emergence of Particle Physics: the

More information

Supersymmetric Gauge Theories, Matrix Models and Geometric Transitions

Supersymmetric Gauge Theories, Matrix Models and Geometric Transitions Supersymmetric Gauge Theories, Matrix Models and Geometric Transitions Frank FERRARI Université Libre de Bruxelles and International Solvay Institutes XVth Oporto meeting on Geometry, Topology and Physics:

More information

Chapters of Advanced General Relativity

Chapters of Advanced General Relativity Chapters of Advanced General Relativity Notes for the Amsterdam-Brussels-Geneva-Paris doctoral school 2014 & 2016 In preparation Glenn Barnich Physique Théorique et Mathématique Université Libre de Bruxelles

More information

TWISTOR DIAGRAMS for Yang-Mills scattering amplitudes

TWISTOR DIAGRAMS for Yang-Mills scattering amplitudes TWISTOR DIAGRAMS for Yang-Mills scattering amplitudes Andrew Hodges Wadham College, University of Oxford London Mathematical Society Durham Symposium on Twistors, Strings and Scattering Amplitudes, 20

More information

MASTER OF SCIENCE IN PHYSICS

MASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCE IN PHYSICS The Master of Science in Physics program aims to develop competent manpower to fill the demands of industry and academe. At the end of the program, the students should have

More information

FYS 3510 Subatomic physics with applications in astrophysics. Nuclear and Particle Physics: An Introduction

FYS 3510 Subatomic physics with applications in astrophysics. Nuclear and Particle Physics: An Introduction FYS 3510 Subatomic physics with applications in astrophysics Nuclear and Particle Physics: An Introduction Nuclear and Particle Physics: An Introduction, 2nd Edition Professor Brian Martin ISBN: 978-0-470-74275-4

More information

Seminar in Wigner Research Centre for Physics. Minkyoo Kim (Sogang & Ewha University) 10th, May, 2013

Seminar in Wigner Research Centre for Physics. Minkyoo Kim (Sogang & Ewha University) 10th, May, 2013 Seminar in Wigner Research Centre for Physics Minkyoo Kim (Sogang & Ewha University) 10th, May, 2013 Introduction - Old aspects of String theory - AdS/CFT and its Integrability String non-linear sigma

More information

If I only had a Brane

If I only had a Brane If I only had a Brane A Story about Gravity and QCD. on 20 slides and in 40 minutes. AdS/CFT correspondence = Anti de Sitter / Conformal field theory correspondence. Chapter 1: String Theory in a nutshell.

More information

Approaches to Quantum Gravity A conceptual overview

Approaches to Quantum Gravity A conceptual overview Approaches to Quantum Gravity A conceptual overview Robert Oeckl Instituto de Matemáticas UNAM, Morelia Centro de Radioastronomía y Astrofísica UNAM, Morelia 14 February 2008 Outline 1 Introduction 2 Different

More information

Possible Advanced Topics Course

Possible Advanced Topics Course Preprint typeset in JHEP style - HYPER VERSION Possible Advanced Topics Course Gregory W. Moore Abstract: Potential List of Topics for an Advanced Topics version of Physics 695, Fall 2013 September 2,

More information

Aspects of (0,2) theories

Aspects of (0,2) theories Aspects of (0,2) theories Ilarion V. Melnikov Harvard University FRG workshop at Brandeis, March 6, 2015 1 / 22 A progress report on d=2 QFT with (0,2) supersymmetry Gross, Harvey, Martinec & Rohm, Heterotic

More information

Top Math-Φ. - Abstract Book - Plenary Lectures. J. Alfaro (PUC, Chile) Mysteries of the Cosmos

Top Math-Φ. - Abstract Book - Plenary Lectures. J. Alfaro (PUC, Chile) Mysteries of the Cosmos Top Math-Φ - Abstract Book - Plenary Lectures J. Alfaro (PUC, Chile) Mysteries of the Cosmos I will review our knowledge of the Universe from the smallest components (Particle Physics) to the largest scales(cosmology)showing

More information

PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in

PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in LONDON BEIJING HONG TSINGHUA Report and Review in Physics Vol2 PRINCIPLES OF PHYSICS From Quantum Field Theory to Classical Mechanics Ni Jun Tsinghua University, China NEW JERSEY \Hp SINGAPORE World Scientific

More information

AdS/CFT duality. Agnese Bissi. March 26, Fundamental Problems in Quantum Physics Erice. Mathematical Institute University of Oxford

AdS/CFT duality. Agnese Bissi. March 26, Fundamental Problems in Quantum Physics Erice. Mathematical Institute University of Oxford AdS/CFT duality Agnese Bissi Mathematical Institute University of Oxford March 26, 2015 Fundamental Problems in Quantum Physics Erice What is it about? AdS=Anti de Sitter Maximally symmetric solution of

More information

A Brief Introduction to AdS/CFT Correspondence

A Brief Introduction to AdS/CFT Correspondence Department of Physics Universidad de los Andes Bogota, Colombia 2011 Outline of the Talk Outline of the Talk Introduction Outline of the Talk Introduction Motivation Outline of the Talk Introduction Motivation

More information

Twistor Strings, Gauge Theory and Gravity. Abou Zeid, Hull and Mason hep-th/

Twistor Strings, Gauge Theory and Gravity. Abou Zeid, Hull and Mason hep-th/ Twistor Strings, Gauge Theory and Gravity Abou Zeid, Hull and Mason hep-th/0606272 Amplitudes for YM, Gravity have elegant twistor space structure: Twistor Geometry Amplitudes for YM, Gravity have elegant

More information

DOWNLOAD PDF NON-PERTURBATIVE METHODS IN 2 DIMENSIONAL QUANTUM FIELD THEORY

DOWNLOAD PDF NON-PERTURBATIVE METHODS IN 2 DIMENSIONAL QUANTUM FIELD THEORY Chapter 1 : CiteSeerX â Two-dimensional Quantum Field Theory, examples and applications The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised

More information

Techniques for exact calculations in 4D SUSY gauge theories

Techniques for exact calculations in 4D SUSY gauge theories Techniques for exact calculations in 4D SUSY gauge theories Takuya Okuda University of Tokyo, Komaba 6th Asian Winter School on Strings, Particles and Cosmology 1 First lecture Motivations for studying

More information

Gauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger. Julius-Maximilians-Universität Würzburg

Gauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger. Julius-Maximilians-Universität Würzburg Gauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger Julius-Maximilians-Universität Würzburg 1 New Gauge/Gravity Duality group at Würzburg University Permanent members 2 Gauge/Gravity

More information

Contents. Appendix A Strong limit and weak limit 35. Appendix B Glauber coherent states 37. Appendix C Generalized coherent states 41

Contents. Appendix A Strong limit and weak limit 35. Appendix B Glauber coherent states 37. Appendix C Generalized coherent states 41 Contents Preface 1. The structure of the space of the physical states 1 1.1 Introduction......................... 1 1.2 The space of the states of physical particles........ 2 1.3 The Weyl Heisenberg algebra

More information

Quantum Physics II (8.05) Fall 2002 Outline

Quantum Physics II (8.05) Fall 2002 Outline Quantum Physics II (8.05) Fall 2002 Outline 1. General structure of quantum mechanics. 8.04 was based primarily on wave mechanics. We review that foundation with the intent to build a more formal basis

More information

Classification of Symmetry Protected Topological Phases in Interacting Systems

Classification of Symmetry Protected Topological Phases in Interacting Systems Classification of Symmetry Protected Topological Phases in Interacting Systems Zhengcheng Gu (PI) Collaborators: Prof. Xiao-Gang ang Wen (PI/ PI/MIT) Prof. M. Levin (U. of Chicago) Dr. Xie Chen(UC Berkeley)

More information

1 September 1997 PEG Event-Symmetry for Superstrings. Philip E. Gibbs

1 September 1997 PEG Event-Symmetry for Superstrings. Philip E. Gibbs 1 September 1997 PEG-16-97 Event-Symmetry for Superstrings Philip E. Gibbs I apply the principle of event-symmetry to simple string models and discuss how these lead to the conviction that multiple quantisation

More information

PUBBLICAZIONI DI ROBERTO CATENACCI. 7) B.Bertotti and R.Catenacci : Effects of gravitational radiation upon

PUBBLICAZIONI DI ROBERTO CATENACCI. 7) B.Bertotti and R.Catenacci : Effects of gravitational radiation upon PUBBLICAZIONI DI ROBERTO CATENACCI 1) B.Bertotti and R.Catenacci : Effects of gravitational radiation upon electromagnetic waves in a dispersive medium. General Relativity and Gravitation, 6, 329-343,

More information

Overview of classical mirror symmetry

Overview of classical mirror symmetry Overview of classical mirror symmetry David Cox (notes by Paul Hacking) 9/8/09 () Physics (2) Quintic 3-fold (3) Math String theory is a N = 2 superconformal field theory (SCFT) which models elementary

More information

Exact Results in D=2 Supersymmetric Gauge Theories And Applications

Exact Results in D=2 Supersymmetric Gauge Theories And Applications Exact Results in D=2 Supersymmetric Gauge Theories And Applications Jaume Gomis Miami 2012 Conference arxiv:1206.2606 with Doroud, Le Floch and Lee arxiv:1210.6022 with Lee N = (2, 2) supersymmetry on

More information

LECTURES ON QUANTUM MECHANICS

LECTURES ON QUANTUM MECHANICS LECTURES ON QUANTUM MECHANICS GORDON BAYM Unitsersity of Illinois A II I' Advanced Bock Progrant A Member of the Perseus Books Group CONTENTS Preface v Chapter 1 Photon Polarization 1 Transformation of

More information

Many-Body Problems and Quantum Field Theory

Many-Body Problems and Quantum Field Theory Philippe A. Martin Francois Rothen Many-Body Problems and Quantum Field Theory An Introduction Translated by Steven Goldfarb, Andrew Jordan and Samuel Leach Second Edition With 102 Figures, 7 Tables and

More information

Physics 4213/5213 Lecture 1

Physics 4213/5213 Lecture 1 August 28, 2002 1 INTRODUCTION 1 Introduction Physics 4213/5213 Lecture 1 There are four known forces: gravity, electricity and magnetism (E&M), the weak force, and the strong force. Each is responsible

More information

Putting String Theory to the Test with AdS/CFT

Putting String Theory to the Test with AdS/CFT Putting String Theory to the Test with AdS/CFT Leopoldo A. Pando Zayas University of Iowa Department Colloquium L = 1 4g 2 Ga µνg a µν + j G a µν = µ A a ν ν A a µ + if a bc Ab µa c ν, D µ = µ + it a

More information

Acknowledgements An introduction to unitary symmetry The search for higher symmetries p. 1 The eight-baryon puzzle p. 1 The elimination of

Acknowledgements An introduction to unitary symmetry The search for higher symmetries p. 1 The eight-baryon puzzle p. 1 The elimination of Preface p. xiii Acknowledgements p. xiv An introduction to unitary symmetry The search for higher symmetries p. 1 The eight-baryon puzzle p. 1 The elimination of G[subscript 0] p. 4 SU(3) and its representations

More information

Contents. 1.1 Prerequisites and textbooks Physical phenomena and theoretical tools The path integrals... 9

Contents. 1.1 Prerequisites and textbooks Physical phenomena and theoretical tools The path integrals... 9 Preface v Chapter 1 Introduction 1 1.1 Prerequisites and textbooks......................... 1 1.2 Physical phenomena and theoretical tools................. 5 1.3 The path integrals..............................

More information

Hamiltonian approach to Yang- Mills Theories in 2+1 Dimensions: Glueball and Meson Mass Spectra

Hamiltonian approach to Yang- Mills Theories in 2+1 Dimensions: Glueball and Meson Mass Spectra Hamiltonian approach to Yang- Mills Theories in 2+1 Dimensions: Glueball and Meson Mass Spectra Aleksandr Yelnikov Virginia Tech based on hep-th/0512200 hep-th/0604060 with Rob Leigh and Djordje Minic

More information

Quark-gluon plasma from AdS/CFT Correspondence

Quark-gluon plasma from AdS/CFT Correspondence Quark-gluon plasma from AdS/CFT Correspondence Yi-Ming Zhong Graduate Seminar Department of physics and Astronomy SUNY Stony Brook November 1st, 2010 Yi-Ming Zhong (SUNY Stony Brook) QGP from AdS/CFT Correspondence

More information

Hadron Physics & Quantum Chromodynamics Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora

Hadron Physics & Quantum Chromodynamics Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora Hadron Physics & Quantum Chromodynamics Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora Hadron Physics & QCD Part 1: First Encounter With Hadrons: Introduction to Mesons & Baryons, The Quark

More information

GROUP THEORY IN PHYSICS

GROUP THEORY IN PHYSICS GROUP THEORY IN PHYSICS Wu-Ki Tung World Scientific Philadelphia Singapore CONTENTS CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 PREFACE INTRODUCTION 1.1 Particle on a One-Dimensional Lattice 1.2 Representations

More information

Diffeomorphism Invariant Gauge Theories

Diffeomorphism Invariant Gauge Theories Diffeomorphism Invariant Gauge Theories Kirill Krasnov (University of Nottingham) Oxford Geometry and Analysis Seminar 25 Nov 2013 Main message: There exists a large new class of gauge theories in 4 dimensions

More information

INTRODUCTION TO THE STRUCTURE OF MATTER

INTRODUCTION TO THE STRUCTURE OF MATTER INTRODUCTION TO THE STRUCTURE OF MATTER A Course in Modern Physics John J. Brehm and William J. Mullin University of Massachusetts Amherst, Massachusetts Fachberelch 5?@8hnlsdie Hochschule Darmstadt! HochschulstraSa

More information

Effective Field Theory for Nuclear Physics! Akshay Vaghani! Mississippi State University!

Effective Field Theory for Nuclear Physics! Akshay Vaghani! Mississippi State University! Effective Field Theory for Nuclear Physics! Akshay Vaghani! Mississippi State University! Overview! Introduction! Basic ideas of EFT! Basic Examples of EFT! Algorithm of EFT! Review NN scattering! NN scattering

More information

Physics 492 Lecture 19

Physics 492 Lecture 19 Physics 492 Lecture 19 Main points of last lecture: Relativistic transformations Four vectors Invarients, Proper time Inner products of vectors Momentum Main points of today s lecture: Momentum Example:

More information

Gravity, Strings and Branes

Gravity, Strings and Branes Gravity, Strings and Branes Joaquim Gomis Universitat Barcelona Miami, 23 April 2009 Fundamental Forces Strong Weak Electromagnetism QCD Electroweak SM Gravity Standard Model Basic building blocks, quarks,

More information

The Hamiltonian formulation of gauge theories

The Hamiltonian formulation of gauge theories The Hamiltonian formulation of gauge theories I [p, q] = dt p i q i H(p, q) " # q i = @H @p i =[q i, H] ṗ i = @H =[p @q i i, H] 1. Symplectic geometry, Hamilton-Jacobi theory,... 2. The first (general)

More information

THE BORDER BETWEEN RELATIVITY AND QUANTUM THEORY

THE BORDER BETWEEN RELATIVITY AND QUANTUM THEORY THE BORDER BETWEEN RELATIVITY AND QUANTUM THEORY Tevian Dray I: Attempts at Unification II: Spinors III: The Future Abstract Many efforts have been made to fulfill Einstein s dream of unifying general

More information

Why we need quantum gravity and why we don t have it

Why we need quantum gravity and why we don t have it Why we need quantum gravity and why we don t have it Steve Carlip UC Davis Quantum Gravity: Physics and Philosophy IHES, Bures-sur-Yvette October 2017 The first appearance of quantum gravity Einstein 1916:

More information

Universal Dynamics from the Conformal Bootstrap

Universal Dynamics from the Conformal Bootstrap Universal Dynamics from the Conformal Bootstrap Liam Fitzpatrick Stanford University! in collaboration with Kaplan, Poland, Simmons-Duffin, and Walters Conformal Symmetry Conformal = coordinate transformations

More information

Lecture Notes on General Relativity

Lecture Notes on General Relativity Lecture Notes on General Relativity Matthias Blau Albert Einstein Center for Fundamental Physics Institut für Theoretische Physik Universität Bern CH-3012 Bern, Switzerland The latest version of these

More information

N = 2 String Amplitudes *

N = 2 String Amplitudes * LBL-37660 August 23, 1995 UCB-PTH-95/30 N = 2 String Amplitudes * Hirosi Oogurit Theoretical Physics Group Lawrence Berkeley Laboratory University of California Berkeley, California 94 720 To appear in

More information

List of Comprehensive Exams Topics

List of Comprehensive Exams Topics List of Comprehensive Exams Topics Mechanics 1. Basic Mechanics Newton s laws and conservation laws, the virial theorem 2. The Lagrangian and Hamiltonian Formalism The Lagrange formalism and the principle

More information

Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction

Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction Lecture 5 Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction WS0/3: Introduction to Nuclear and Particle Physics,, Part I I. Angular Momentum Operator Rotation R(θ): in polar coordinates the

More information

Particle Physics Lecture 1 : Introduction Fall 2015 Seon-Hee Seo

Particle Physics Lecture 1 : Introduction Fall 2015 Seon-Hee Seo Particle Physics Lecture 1 : Introduction Fall 2015 Seon-Hee Seo Particle Physics Fall 2015 1 Course Overview Lecture 1: Introduction, Decay Rates and Cross Sections Lecture 2: The Dirac Equation and Spin

More information

Exact anomalous dimensions of 4-dimensional N=4 super-yang-mills theory in 'thooft limit

Exact anomalous dimensions of 4-dimensional N=4 super-yang-mills theory in 'thooft limit PACIFIC 2015 UCLA Symposium on Particle Astrophysics and Cosmology Including Fundamental Interactions September 12-19, 2015, Moorea, French Polynesia Exact anomalous dimensions of 4-dimensional N=4 super-yang-mills

More information

Study Plan for Ph.D in Physics (2011/2012)

Study Plan for Ph.D in Physics (2011/2012) Plan Study Plan for Ph.D in Physics (2011/2012) Offered Degree: Ph.D in Physics 1. General Rules and Conditions:- This plan conforms to the regulations of the general frame of the higher graduate studies

More information

Non-Geometric Calabi- Yau Backgrounds

Non-Geometric Calabi- Yau Backgrounds Non-Geometric Calabi- Yau Backgrounds CH, Israel and Sarti 1710.00853 A Dabolkar and CH, 2002 Duality Symmetries Supergravities: continuous classical symmetry, broken in quantum theory, and by gauging

More information

Part I. Many-Body Systems and Classical Field Theory

Part I. Many-Body Systems and Classical Field Theory Part I. Many-Body Systems and Classical Field Theory 1. Classical and Quantum Mechanics of Particle Systems 3 1.1 Introduction. 3 1.2 Classical Mechanics of Mass Points 4 1.3 Quantum Mechanics: The Harmonic

More information

Or: what symmetry can teach us about quantum gravity and the unification of physics. Technische Universität Dresden, 5 July 2011

Or: what symmetry can teach us about quantum gravity and the unification of physics. Technische Universität Dresden, 5 July 2011 bla Symmetry and Unification Or: what symmetry can teach us about quantum gravity and the unification of physics. Technische Universität Dresden, 5 July 2011 Hermann Nicolai MPI für Gravitationsphysik,

More information

Lecture Notes. Quantum Theory. Prof. Maximilian Kreuzer. Institute for Theoretical Physics Vienna University of Technology. covering the contents of

Lecture Notes. Quantum Theory. Prof. Maximilian Kreuzer. Institute for Theoretical Physics Vienna University of Technology. covering the contents of Lecture Notes Quantum Theory by Prof. Maximilian Kreuzer Institute for Theoretical Physics Vienna University of Technology covering the contents of 136.019 Quantentheorie I and 136.027 Quantentheorie II

More information

Clebsch-Gordan Coefficients

Clebsch-Gordan Coefficients Phy489 Lecture 7 Clebsch-Gordan Coefficients 2 j j j2 m m m 2 j= j j2 j + j j m > j m > = C jm > m = m + m 2 2 2 Two systems with spin j and j 2 and z components m and m 2 can combine to give a system

More information

Classical aspects of Poincaré gauge theory of gravity

Classical aspects of Poincaré gauge theory of gravity Classical aspects of Poincaré gauge theory of gravity Jens Boos jboos@perimeterinstitute.ca Perimeter Institute for Theoretical Physics Wednesday, Nov 11, 2015 Quantum Gravity group meeting Perimeter Institute

More information

HIGHER SPIN PROBLEM IN FIELD THEORY

HIGHER SPIN PROBLEM IN FIELD THEORY HIGHER SPIN PROBLEM IN FIELD THEORY I.L. Buchbinder Tomsk I.L. Buchbinder (Tomsk) HIGHER SPIN PROBLEM IN FIELD THEORY Wroclaw, April, 2011 1 / 27 Aims Brief non-expert non-technical review of some old

More information

Lecture notes for QFT I (662)

Lecture notes for QFT I (662) Preprint typeset in JHEP style - PAPER VERSION Lecture notes for QFT I (66) Martin Kruczenski Department of Physics, Purdue University, 55 Northwestern Avenue, W. Lafayette, IN 47907-036. E-mail: markru@purdue.edu

More information

arxiv:hep-ph/ v1 8 Feb 2000

arxiv:hep-ph/ v1 8 Feb 2000 Gravity, Particle Physics and their Unification 1 J. M. Maldacena Department of Physics Harvard University, Cambridge, Massachusetts 02138 arxiv:hep-ph/0002092v1 8 Feb 2000 1 Introduction Our present world

More information

Topics for the Qualifying Examination

Topics for the Qualifying Examination Topics for the Qualifying Examination Quantum Mechanics I and II 1. Quantum kinematics and dynamics 1.1 Postulates of Quantum Mechanics. 1.2 Configuration space vs. Hilbert space, wave function vs. state

More information

Lecture 2: 3d gravity as group theory Quantum Coulomb Solution

Lecture 2: 3d gravity as group theory Quantum Coulomb Solution The Second Mandelstam Theoretical Physics School University of the Witwatersrand 17/01/2018 Lecture 2: 3d gravity as group theory Quantum Coulomb Solution Glenn Barnich Physique théorique et mathématique

More information

Quantising Gravitational Instantons

Quantising Gravitational Instantons Quantising Gravitational Instantons Kirill Krasnov (Nottingham) GARYFEST: Gravitation, Solitons and Symmetries MARCH 22, 2017 - MARCH 24, 2017 Laboratoire de Mathématiques et Physique Théorique Tours This

More information

Ruben Sandapen (Acadia & Mt. A) in collaboration with M. Ahmady & F. Chishtie. September 5 th 2016

Ruben Sandapen (Acadia & Mt. A) in collaboration with M. Ahmady & F. Chishtie. September 5 th 2016 Holographic Distribution Amplitudes for mesons Ruben Sandapen (Acadia & Mt. A) in collaboration with M. Ahmady & F. Chishtie Diffraction 2016 Progress in QCD session September 5 th 2016 1 Outline Overview

More information

Three Applications of Topology to Physics

Three Applications of Topology to Physics Three Applications of Topology to Physics Dan Freed University of Texas at Austin January 12, 2018 Problem 1: Invertible Phases of Matter Fix discrete parameters for quantum system: dimension, symmetry

More information

Departement de Physique Theorique, Universite de Geneve, Abstract

Departement de Physique Theorique, Universite de Geneve, Abstract hep-th/950604 A NOTE ON THE STRING ANALOG OF N = SUPER-SYMMETRIC YANG-MILLS Cesar Gomez 1 and Esperanza Lopez 1 Departement de Physique Theorique, Universite de Geneve, Geneve 6, Switzerland Abstract A

More information

String cosmology and the index of the Dirac operator

String cosmology and the index of the Dirac operator String cosmology and the index of the Dirac operator Renata Kallosh Stanford STRINGS 2005 Toronto, July 12 Outline String Cosmology, Flux Compactification,, Stabilization of Moduli, Metastable de Sitter

More information

First structure equation

First structure equation First structure equation Spin connection Let us consider the differential of the vielbvein it is not a Lorentz vector. Introduce the spin connection connection one form The quantity transforms as a vector

More information

Manifestly diffeomorphism invariant classical Exact Renormalization Group

Manifestly diffeomorphism invariant classical Exact Renormalization Group Manifestly diffeomorphism invariant classical Exact Renormalization Group Anthony W. H. Preston University of Southampton Supervised by Prof. Tim R. Morris Talk prepared for Asymptotic Safety seminar,

More information

Symmetries, Groups Theory and Lie Algebras in Physics

Symmetries, Groups Theory and Lie Algebras in Physics Symmetries, Groups Theory and Lie Algebras in Physics M.M. Sheikh-Jabbari Symmetries have been the cornerstone of modern physics in the last century. Symmetries are used to classify solutions to physical

More information

PHYSICS-PH (PH) Courses. Physics-PH (PH) 1

PHYSICS-PH (PH) Courses. Physics-PH (PH) 1 Physics-PH (PH) 1 PHYSICS-PH (PH) Courses PH 110 Physics of Everyday Phenomena (GT-SC2) Credits: 3 (3-0-0) Fundamental concepts of physics and elementary quantitative reasoning applied to phenomena in

More information

MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont

MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont McGRAW-HILL, INC. New York St. Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico Milan Montreal New Delhi

More information

Topics in Geometry: Mirror Symmetry

Topics in Geometry: Mirror Symmetry MIT OpenCourseWare http://ocw.mit.edu 18.969 Topics in Geometry: Mirror Symmetry Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MIRROR SYMMETRY:

More information

String-Theory: Open-closed String Moduli Spaces

String-Theory: Open-closed String Moduli Spaces String-Theory: Open-closed String Moduli Spaces Heidelberg, 13.10.2014 History of the Universe particular: Epoch of cosmic inflation in the early Universe Inflation and Inflaton φ, potential V (φ) Possible

More information

Knot Homology from Refined Chern-Simons Theory

Knot Homology from Refined Chern-Simons Theory Knot Homology from Refined Chern-Simons Theory Mina Aganagic UC Berkeley Based on work with Shamil Shakirov arxiv: 1105.5117 1 the knot invariant Witten explained in 88 that J(K, q) constructed by Jones

More information

Heterotic Torsional Backgrounds, from Supergravity to CFT

Heterotic Torsional Backgrounds, from Supergravity to CFT Heterotic Torsional Backgrounds, from Supergravity to CFT IAP, Université Pierre et Marie Curie Eurostrings@Madrid, June 2010 L.Carlevaro, D.I. and M. Petropoulos, arxiv:0812.3391 L.Carlevaro and D.I.,

More information

Connection Variables in General Relativity

Connection Variables in General Relativity Connection Variables in General Relativity Mauricio Bustamante Londoño Instituto de Matemáticas UNAM Morelia 28/06/2008 Mauricio Bustamante Londoño (UNAM) Connection Variables in General Relativity 28/06/2008

More information

The Role Of Magnetic Monopoles In Quark Confinement (Field Decomposition Approach)

The Role Of Magnetic Monopoles In Quark Confinement (Field Decomposition Approach) The Role Of Magnetic Monopoles In Quark Confinement (Field Decomposition Approach) IPM school and workshop on recent developments in Particle Physics (IPP11) 2011, Tehran, Iran Sedigheh Deldar, University

More information

Derivation of Electro Weak Unification and Final Form of Standard Model with QCD and Gluons 1 W W W 3

Derivation of Electro Weak Unification and Final Form of Standard Model with QCD and Gluons 1 W W W 3 Derivation of Electro Weak Unification and Final Form of Standard Model with QCD and Gluons 1 W 1 + 2 W 2 + 3 W 3 Substitute B = cos W A + sin W Z 0 Sum over first generation particles. up down Left handed

More information

Three Descriptions of the Cohomology of Bun G (X) (Lecture 4)

Three Descriptions of the Cohomology of Bun G (X) (Lecture 4) Three Descriptions of the Cohomology of Bun G (X) (Lecture 4) February 5, 2014 Let k be an algebraically closed field, let X be a algebraic curve over k (always assumed to be smooth and complete), and

More information

Towards a manifestly diffeomorphism invariant Exact Renormalization Group

Towards a manifestly diffeomorphism invariant Exact Renormalization Group Towards a manifestly diffeomorphism invariant Exact Renormalization Group Anthony W. H. Preston University of Southampton Supervised by Prof. Tim R. Morris Talk prepared for UK QFT-V, University of Nottingham,

More information

Relativity, Gravitation, and Cosmology

Relativity, Gravitation, and Cosmology Relativity, Gravitation, and Cosmology A basic introduction TA-PEI CHENG University of Missouri St. Louis OXFORD UNIVERSITY PRESS Contents Parti RELATIVITY Metric Description of Spacetime 1 Introduction

More information

B. PHENOMENOLOGICAL NUCLEAR MODELS

B. PHENOMENOLOGICAL NUCLEAR MODELS B. PHENOMENOLOGICAL NUCLEAR MODELS B.0. Basic concepts of nuclear physics B.0. Binding energy B.03. Liquid drop model B.04. Spherical operators B.05. Bohr-Mottelson model B.06. Intrinsic system of coordinates

More information

Isospin. H. A. Tanaka

Isospin. H. A. Tanaka Isospin H. A. Tanaka Announcements Problem Set due today at 5 PM Box #7 in basement of McLennan Problem set will be posted today The Nobel Prize in Physics 05 The Royal Swedish Academy of Sciences has

More information

Enumerative Invariants in Algebraic Geometry and String Theory

Enumerative Invariants in Algebraic Geometry and String Theory Dan Abramovich -. Marcos Marino Michael Thaddeus Ravi Vakil Enumerative Invariants in Algebraic Geometry and String Theory Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy June 6-11,

More information

Anomaly. Kenichi KONISHI University of Pisa. College de France, 14 February 2006

Anomaly. Kenichi KONISHI University of Pisa. College de France, 14 February 2006 Anomaly Kenichi KONISHI University of Pisa College de France, 14 February 2006 Abstract Symmetry and quantization U A (1) anomaly and π 0 decay Origin of anomalies Chiral and nonabelian anomaly Anomally

More information

N=1 Global Supersymmetry in D=4

N=1 Global Supersymmetry in D=4 Susy algebra equivalently at quantum level Susy algebra In Weyl basis In this form it is obvious the U(1) R symmetry Susy algebra We choose a Majorana representation for which all spinors are real. In

More information