Symmetry Groups conservation law quantum numbers Gauge symmetries local bosons mediate the interaction Group Abelian Product of Groups simple


 Barbra Davis
 1 years ago
 Views:
Transcription
1 Symmetry Groups Symmetry plays an essential role in particle theory. If a theory is invariant under transformations by a symmetry group one obtains a conservation law and quantum numbers. For example, invariance under rotation in space leads to angular momentum conservation and to the quantum numbers j, m j for the total angular momentum. Gauge symmetries: These are local symmetries that act differently at each spacetime point x µ = (t,x). They create particularly stringent constraints on the structure of a theory. For example, gauge symmetry automatically determines the interaction between particles by introducing bosons that mediate the interaction. All current models of elementary particles incorporate gauge symmetry. (Details on p. 4) Groups: A group G consists of elements a, inverse elements a 1, a unit element 1, and a multiplication rule with the properties: 1. If a,b are in G, then c = a b is in G. 2. a (b c) = (a b) c 3. a 1 = 1 a = a 4. a a 1 = a 1 a = 1 The group is called Abelian if it obeys the additional commutation law: 5. a b = b a Product of Groups: The product group G H of two groups G, H is defined by pairs of elements with the multiplication rule (g 1,h 1 ) (g 2,h 2 ) = (g 1 g 2, h 1 h 2 ). A group is called simple if it cannot be decomposed into a product of two other groups. (Compare a prime number as analog.) If a group is not simple, consider the factor groups. Examples: n n matrices of complex numbers with matrix multiplication. Hermitian: M = M (M = M T *, T = transpose, * = complex conjugate) Unitary: U = U 1 Special: S = 1 (determinant = 1) 1
2 U(n) : The group of complex, unitary n n matrices U(n) = SU(n) U(1) for n>1 (not a simple group) U(1) The complex unit circle: U = z = exp[iϕ], ϕ real U U = z*z = z 2 = 1 Gauge symmetry transformation: ψ (x,t) = exp[ iϕ(x,t)] ψ(x,t) Probability conserved: ψ * ψ = ψ* ψ U(1) EM describes the electromagnetic interaction. 1 boson photon A 1 quantum number charge Q SU(n): The group of complex, unitary n n matrices with determinant 1 Generate a unitary matrix U from a Hermitian matrix H: U = exp[ih] = Σ m H m /m! Write all Hermitian matrices using a basis set J i = generators : H = Σ i ϕ i J i Use a basis set J i that guarantees U =1: trace(j i ) = 0 (n 2 1) matrices J i (n 2 1) gauge bosons A i (n 1) diagonal J i (n 1) quantum numbers Gauge transformation: ψ (x,t) = U ψ(x,t) = exp[ Σ i ϕ i (x,t) J i ] ψ(x,t) Probability conserved: ψ * ψ = (Uψ)* (Uψ) = ψ*u Uψ = ψ* ψ SU(2) describes the (broken) Isospin symmetry of the Weak Interaction. 3 Pauli matrices σ i J i = σ i / 2 3 bosons W +,W,Z 1 diagonal J i J 3 (zcomponent of the isospin) SU(3) describes the (exact) Color symmetry of the Strong Interaction. 8 GellMann matrices λ i J i = λ i / 2 8 bosons Gluons G 1, G 8 2 diagonal J i J 3, J 8 (two independent colors) SU(5) is a grand unification group which contains the standard model. 2
3 SU(3) SU(2) U(1) Y Standard Model Color + Isospin + Hypercharge SU(2) U(1) Y ElectroWeak Interaction Isospin + Hypercharge J 3 Y = 2 (Q J 3 ) U(1) EM Electromagnetic Charge Q SU(2) U(1) Y breaks down to the electromagnetic U(1) EM (see p. 4). Pauli Matrices: GellMann Matrices: = Pauli matrices + rows and columns of zeros σ 1 = λ 1 = λ 4 = λ 6 = σ 2 = 0 i i 0 λ 2 = 0 i 0 i 0 0 λ 5 = 0 0 i i 0 0 λ 7 = 0 0 i 0 i 0 σ 3 = λ 3 = Select two independent matrices from the last row. λ 8 = /
4 Gauge Bosons: Conceptually, all of today s particle theories start out with a set of fermions, for example the electron in quantum electrodynamics. Fermions are represented by a wave function ψ. One then postulates gauge invariance, i.e., the gauge transformation ψ = exp[ iϕ(x µ )] ψ should leave the theory invariant. That is fine for the probability density ψ*ψ but the wave equation is not invariant. An unwanted extra term is created by the derivative of the phase factor ϕ(x µ ). Derivatives are related to the momentum operator, for example p 2 /2m e = 2 /2m e in the Schrödinger equation and p µ = i µ in the Dirac equation (448 quantum notes, p. 17). The theory can be made gauge invariant by adding the electromagnetic fourpotential A µ to the fourmomentum p µ in order to cancel the phase derivative. The A µ are the wave functions of the photon, the boson that describes the electromagnetic interaction. The complete gauge transformation of the wave function ψ for the electron and the A µ for the photon becomes: ψ = exp[ iϕ] ψ ћ,c = 1 A µ = A µ + q 1 µ ϕ µ = / x µ q = electric charge = e for the electron p µ = i µ q A µ p µ = momentum operator = generalized covariant derivative With these definitions one has gaugeinvariance for the probability density ψ*ψ and for the Dirac equation: ψ *ψ = ψ ψ γ µ p µ ψ = m e ψ γ µ p µ ψ = m e ψ In similar fashion one can incorporate the electromagnetic interaction into the Schrödinger equation using the energy and momentum operators E and p : E = +i / t q Φ E ψ = p 2 /2m e ψ p = i / x q A p µ = (Ε, p), x µ = (t,x), A µ = (Φ, A) For larger groups the momentum operator and the gaugeinvariant derivative involve a product of several group generators J i and the corresponding gauge bosons A i µ : p µ = i µ + g Σ i J i A i µ g = generalized charge, g 2 /4π = coupling constant There is a parallel to the definition of the covariant derivative D µ in general relativity: D µ A ν = µ A ν + Γ ν µλ A λ 4
5 The first term describes the change of A ν, the second term the change of the coordinate system from one spacetime point to the next. The wave equation for the gauge bosons, i.e.. the generalization of the Maxwell equations, can be derived by forming a gaugeinvariant field tensor using the generalized derivative. For nonabelian symmetry groups (e.g. SU(2), SU(3) ) the wave equations become more interesting because they imply interactions between the gauge bosons themselves, not just a mediation of the interaction between fermions. Symmetry Breaking: Gauge symmetries are often broken, but in a subtle way. The fundamental equations are symmetric, but the ground state wave function breaks the symmetry. An analog is a ferromagnetic ground state, where the rotational symmetry of the electromagnetic interaction is broken by a specific spin orientation of the ferromagnet ( spontaneous symmetry breaking ). When a gauge symmetry is broken the gauge bosons are able to acquire an effective mass, even though gauge symmetry does not allow a boson mass in the fundamental equations. The breakdown of the electroweak symmetry SU(2) U(1) Y converts the 4 massless gauge bosons A 1,A 2,A 3, and B of the symmetric theory into the 3 massive bosons W +,W,Z of the weak interaction and the massless photon A of the electromagnetic interaction (which represents the remaining symmetry). The conversion can be broken up into two steps. First, combinations with welldefined isospin J 3 = ±1 are formed: W + = (A 1 ± i A 2 ) / 2 Then, A 3 is mixed with the gauge boson B of U(1) Y : Z = cosϑ W sinϑ W A 3 A sinϑ W cosϑ W B The resulting observed particles are the Z and photon A. The weak mixing angle ϑ W is determined by the ratio of the coupling constants g for SU(2) and g for U(1) Y : tan ϑ W = g /g 5
6 SU(3) Color: 8 gauge bosons G i are associated with the 8 generators J i = λ i / 2. The bosons are the 8 gluons that mediate the strong interaction. Define three color quantum numbers, plus three complementary colors for antiparticles: R = red G = green B = blue R = G+B = cyan G = R+B = magenta B = R+G = yellow The quarkgluon interaction transfers color from one quark to another (see the diagram). Therefore, gluons carry two color indices, which can be assigned to rows and columns of the GellMann matrices λ i : R G B R * * * G * * * for example G RG : = (λ 1 + i λ 2 )/2 B * * * q G q R G RG The SU(3) color symmetry forces all hadrons to be white, i.e., all color quantum numbers are zero. That can be achieved with the following combinations of quarks q and antiquarks q: qq = 1/ 3 [q R q R + q G q G + q B q B ] = 1/ 3 Σ ik δ ik q i q k meson, symmetric qqq = 1/ 6 [ +q R q G q B q B q G q R = 1/ 6 Σ ijk ε ijk q i q j q k baryon, antisymmetric +q B q R q G q G q R q B +q G q B q R q R q B q G ] when exchanging color indices of two particles. even odd permutation SU(3) Eightfold Way : This is a SU(3) symmetry completely different from color SU(3), and it is only approximate. It describes the assembly of the up, down, and strange quarks into hadrons. Instead of three quark colors one has three quark flavors. This symmetry leaves out the other three quarks (charmed, bottom, and top) and ignores mass differences between the quarks. 6
7 Supersymmetry: Spacetime has two basic symmetries, translation and rotation. The rotational symmetry can be divided into spatial rotations and mixed spacetime rotations, the Lorentz transformations. The combination of all these symmetries forms the Poincare group. There is only one extension of the Poincare group that is consistent with basic principles, and that is supersymmetry. In addition to the normal spacetime coordinates one introduces anticommuting coordinates, which cannot be described by ordinary numbers. Supersymmetry requires that each particle is paired with a superpartner, a fermion with a boson and vice versa. Supersymmetric theories are even more constrained than gauge theories, and divergent terms in a perturbation expansion tend to be cancelled out because two superpartners contribute with opposite signs. None of the superpartners of existing particles have been found yet, which means that supersymmetry is certainly broken. Nevertheless, it looks promising as a symmetry at very high energies, where it allows a unification of the three coupling constants of the standard model into one universal coupling constant. Figure: Extrapolation of the inverse coupling constants α 1 towards higher energies µ for the standard model (left) and for its supersymmetric extension (right). All coupling constants become equal at the same energy, and that energy is not too far from the Planck energy, the fundamental energy scale obtained from ћ,c, and the gravitational constant. 7
wave functions PhD seminar FZ Juelich, Feb 2013
SU(3) symmetry and Baryon wave functions Sedigheh Jowzaee PhD seminar FZ Juelich, Feb 2013 Introduction Fundamental symmetries of our universe Symmetry to the quark model: Hadron wave functions q q Existence
More informationSymmetries, Groups, and Conservation Laws
Chapter Symmetries, Groups, and Conservation Laws The dynamical properties and interactions of a system of particles and fields are derived from the principle of least action, where the action is a 4dimensional
More informationREVIEW. Quantum electrodynamics (QED) Quantum electrodynamics is a theory of photons interacting with the electrons and positrons of a Dirac field:
Quantum electrodynamics (QED) based on S58 Quantum electrodynamics is a theory of photons interacting with the electrons and positrons of a Dirac field: Noether current of the lagrangian for a free Dirac
More informationKern und Teilchenphysik I Lecture 13:Quarks and QCD
Kern und Teilchenphysik I Lecture 13:Quarks and QCD (adapted from the Handout of Prof. Mark Thomson) Prof. Nico Serra Dr. Patrick Owen, Dr. Silva Coutinho http://www.physik.uzh.ch/de/lehre/phy211/hs2016.html
More informationFunctional determinants
Functional determinants based on S53 We are going to discuss situations where a functional determinant depends on some other field and so it cannot be absorbed into the overall normalization of the path
More information2.4 Parity transformation
2.4 Parity transformation An extremely simple group is one that has only two elements: {e, P }. Obviously, P 1 = P, so P 2 = e, with e represented by the unit n n matrix in an n dimensional representation.
More informationAn Introduction to Particle Physics
An Introduction to Particle Physics The Universe started with a Big Bang The Universe started with a Big Bang What is our Universe made of? Particle physics aims to understand Elementary (fundamental)
More informationTHE STANDARD MODEL AND THE GENERALIZED COVARIANT DERIVATIVE
THE STANDAD MODEL AND THE GENEALIZED COVAIANT DEIVATIVE arxiv:hepph/9907480v Jul 999 M. Chaves and H. Morales Escuela de Física, Universidad de Costa ica San José, Costa ica Emails: mchaves@cariari.ucr.ac.cr,
More informationWeak interactions and vector bosons
Weak interactions and vector bosons What do we know now about weak interactions? Theory of weak interactions Fermi's theory of weak interactions VA theory Current  current theory, current algebra W and
More informationOption 212: UNIT 2 Elementary Particles
Department of Physics and Astronomy Option 212: UNIT 2 Elementary Particles SCHEDULE 26Jan15 13.00pm LRB Intro lecture 28Jan15 12.00pm LRB Problem solving (2Feb15 10.00am E Problem Workshop) 4Feb15
More informationOUTLINE. CHARGED LEPTONIC WEAK INTERACTION  Decay of the Muon  Decay of the Neutron  Decay of the Pion
Weak Interactions OUTLINE CHARGED LEPTONIC WEAK INTERACTION  Decay of the Muon  Decay of the Neutron  Decay of the Pion CHARGED WEAK INTERACTIONS OF QUARKS  CabibboGIM Mechanism  CabibboKobayashiMaskawa
More informationBack to Gauge Symmetry. The Standard Model of Par0cle Physics
Back to Gauge Symmetry The Standard Model of Par0cle Physics Laws of physics are phase invariant. Probability: P = ψ ( r,t) 2 = ψ * ( r,t)ψ ( r,t) Unitary scalar transformation: U( r,t) = e iaf ( r,t)
More informationNotes on SU(3) and the Quark Model
Notes on SU() and the Quark Model Contents. SU() and the Quark Model. Raising and Lowering Operators: The Weight Diagram 4.. Triangular Weight Diagrams (I) 6.. Triangular Weight Diagrams (II) 8.. Hexagonal
More informationOutline. Charged Leptonic Weak Interaction. Charged Weak Interactions of Quarks. Neutral Weak Interaction. Electroweak Unification
Weak Interactions Outline Charged Leptonic Weak Interaction Decay of the Muon Decay of the Neutron Decay of the Pion Charged Weak Interactions of Quarks CabibboGIM Mechanism CabibboKobayashiMaskawa
More informationLecture 3: Quarks and Symmetry in Quarks
Lecture 3: Quarks and Symmetry in Quarks Quarks Cross Section, Fermions & Bosons, Wave Eqs. Symmetry: Rotation, Isospin (I), Parity (P), Charge Conjugate (C), SU(3), Gauge symmetry Conservation Laws: http://faculty.physics.tamu.edu/kamon/teaching/phys627/
More informationModern physics 1 Chapter 13
Modern physics 1 Chapter 13 13. Particle physics Particle studied within the ATLASproject CERN In the beginning of 1930, it seemed that all the physics fundaments was placed within the new areas of elementary
More informationGoldstone Bosons and Chiral Symmetry Breaking in QCD
Goldstone Bosons and Chiral Symmetry Breaking in QCD Michael Dine Department of Physics University of California, Santa Cruz May 2011 Before reading this handout, carefully read Peskin and Schroeder s
More informationSpontaneous breaking of supersymmetry
Spontaneous breaking of supersymmetry Hiroshi Suzuki Theoretical Physics Laboratory Nov. 18, 2009 @ Theoretical science colloquium in RIKEN Hiroshi Suzuki (TPL) Spontaneous breaking of supersymmetry Nov.
More information3 Quantization of the Dirac equation
3 Quantization of the Dirac equation 3.1 Identical particles As is well known, quantum mechanics implies that no measurement can be performed to distinguish particles in the same quantum state. Elementary
More informationIsospin. K.K. Gan L5: Isospin and Parity 1
Isospin Isospin is a continuous symmetry invented by Heisenberg: Explain the observation that the strong interaction does not distinguish between neutron and proton. Example: the mass difference between
More informationQuark Model History and current status
Quark Model History and current status Manon Bischoff HeavyIon Seminar 2013 October 31, 2013 Manon Bischoff Quark Model 1 Outline Introduction Motivation and historical development Group theory and the
More informationIX. Electroweak unification
IX. Electroweak unification The problem of divergence A theory of weak interactions only by means of W ± bosons leads to infinities e + e  γ W  W + e + W + ν e ν µ e  W  µ + µ Divergent integrals Figure
More informationThe God particle at last? Astronomy Ireland, Oct 8 th, 2012
The God particle at last? Astronomy Ireland, Oct 8 th, 2012 Cormac O Raifeartaigh Waterford Institute of Technology CERN July 4 th 2012 (ATLAS and CMS ) A new particle of mass 125 GeV I The Higgs boson
More informationParticle Physics. Dr Victoria Martin, Spring Semester 2012 Lecture 1: The Mysteries of Particle Physics, or Why should I take this course?
Particle Physics Dr Victoria Martin, Spring Semester 2012 Lecture 1: The Mysteries of Particle Physics, or Why should I take this course? Contents: Review of the Standard Model! What we know! What we don
More informationLecture III: Higgs Mechanism
ecture III: Higgs Mechanism Spontaneous Symmetry Breaking The Higgs Mechanism Mass Generation for eptons Quark Masses & Mixing III.1 Symmetry Breaking One example is the infinite ferromagnet the nearest
More informationContinuous symmetries and conserved currents
Continuous symmetries and conserved currents based on S22 Consider a set of scalar fields, and a lagrangian density let s make an infinitesimal change: variation of the action: setting we would get equations
More informationAnomalies and discrete chiral symmetries
Anomalies and discrete chiral symmetries Michael Creutz BNL & U. Mainz Three sources of chiral symmetry breaking in QCD spontaneous breaking ψψ 0 explains lightness of pions implicit breaking of U(1) by
More informationThe God particle at last? Science Week, Nov 15 th, 2012
The God particle at last? Science Week, Nov 15 th, 2012 Cormac O Raifeartaigh Waterford Institute of Technology CERN July 4 th 2012 (ATLAS and CMS ) A new particle of mass 125 GeV Why is the Higgs particle
More information12.2 Problem Set 2 Solutions
78 CHAPTER. PROBLEM SET SOLUTIONS. Problem Set Solutions. I will use a basis m, which ψ C = iγ ψ = Cγ ψ (.47) We can define left (light) handed Majorana fields as, so that ω = ψ L + (ψ L ) C (.48) χ =
More informationQED and the Standard Model Autumn 2014
QED and the Standard Model Autumn 2014 Joel Goldstein University of Bristol Joel.Goldstein@bristol.ac.uk These lectures are designed to give an introduction to the gauge theories of the standard model
More informationGauge Theory of ElectroWeak Interactions. Following slides based among others on
Gauge Theory of ElectroWeak Interactions Read Appendix D of Book Gauge Theories Following slides based among others on The ideas of particle physics: an introduction to scientists, by Coughlan, Dodd,
More informationg abφ b = g ab However, this is not true for a local, or spacetime dependant, transformations + g ab
YangMills theory Modern particle theories, such as the Standard model, are quantum Yang Mills theories. In a quantum field theory, spacetime fields with relativistic field equations are quantized and,
More informationarxiv:hepph/ v1 1 Feb 2005
Vector Goldstone Boson and Lorentz Invariance arxiv:hepph/050011v1 1 Feb 005 LingFong Li Department of Physics, Carnegie Mellon University, Pittsburgh, PA 1513 January 5, 018 Abstract Spontanous symmetry
More informationDirac Equation. Chapter 1
Chapter Dirac Equation This course will be devoted principally to an exposition of the dynamics of Abelian and nonabelian gauge theories. These form the basis of the Standard Model, that is, the theory
More informationT 1! p k. = T r! k., s k. ', x' ] = i!, s y. ', s y
Time Reversal r k ' = r k = T r k T 1 p k ' = p k, s k ' = s k T cannot be represented by an unitary operator. Unitary opera$ons preserve algebraic rela$ons between operators, while T changes the sign
More informationPhysics 7730: Particle Physics
Physics 7730: Particle Physics! Instructor: Kevin Stenson (particle physics experimentalist)! Office: Duane F317 (Gamow tower)! Email: kevin.stenson@colorado.edu! Phone: 3034921106! Web page: http://wwwhep.colorado.edu/~stenson/!
More informationQuantum 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 informationQuantum Field Theory
Quantum Field Theory PHYSP 621 Radovan Dermisek, Indiana University Notes based on: M. Srednicki, Quantum Field Theory 1 Attempts at relativistic QM based on S1 A proper description of particle physics
More informationCurrent knowledge tells us that matter is made of fundamental particle called fermions,
Chapter 1 Particle Physics 1.1 Fundamental Particles Current knowledge tells us that matter is made of fundamental particle called fermions, which are spin 1 particles. Our world is composed of two kinds
More informationCoupling of Angular Momenta Isospin NucleonNucleon Interaction
Lecture 5 Coupling of Angular Momenta Isospin NucleonNucleon Interaction WS0/3: Introduction to Nuclear and Particle Physics,, Part I I. Angular Momentum Operator Rotation R(θ): in polar coordinates the
More informationA short overview on strong interaction and quantum chromodynamics
A short overview on strong interaction and quantum chromodynamics Christoph Klein Universität Siegen Doktorandenseminar 08.10.2008 Christoph Klein (Universität Siegen) QCD and strong interaction Doktorandenseminar
More informationContents. 3 Protons and Other Hadrons in Quark Model Probing the Parton Structure in the Proton 37. iii
Contents 1 Introduction to QCD and the Standard Model 1 1.1 Quarks............................................ 1 1.2 Gluons and Quantum Chromodynamics......................... 3 1.3 Force Between Quarks,
More informationString / gauge theory duality and ferromagnetic spin chains
String / gauge theory duality and ferromagnetic spin chains M. Kruczenski Princeton Univ. In collaboration w/ Rob Myers, David Mateos, David Winters Arkady Tseytlin, Anton Ryzhov Summary Introduction mesons,,...
More informationTwo Fundamental Principles of Nature s Interactions
Two Fundamental Principles of Nature s Interactions Tian Ma, Shouhong Wang Supported in part by NSF, ONR and Chinese NSF http://www.indiana.edu/ fluid I. Gravity and Principle of Interaction Dynamics PID)
More informationThe mass of the Higgs boson
The mass of the Higgs boson LHC : Higgs particle observation CMS 2011/12 ATLAS 2011/12 a prediction Higgs boson found standard model Higgs boson T.Plehn, M.Rauch Spontaneous symmetry breaking confirmed
More informationAstronomy 182: Origin and Evolution of the Universe
Astronomy 182: Origin and Evolution of the Universe Prof. Josh Frieman Lecture 12 Nov. 18, 2015 Today Big Bang Nucleosynthesis and Neutrinos Particle Physics & the Early Universe Standard Model of Particle
More informationCavendish Laboratory Institute of Astronomy
Andy Parker George Efstathiou Cavendish Laboratory Institute of Astronomy This is a 16 lecture Part III Minor Option. Tuesdays and Thursdays 10 am Textbooks: Perkins Particle Astrophysics Bergstrom and
More informationQFT. Unit 1: Relativistic Quantum Mechanics
QFT Unit 1: Relativistic Quantum Mechanics What s QFT? Relativity deals with things that are fast Quantum mechanics deals with things that are small QFT deals with things that are both small and fast What
More informationarxiv:hepph/ v1 23 Jun 1999
Why do we have parity violation? GUTPA/99/05/2 arxiv:hepph/9906466v1 23 Jun 1999 C.D. Froggatt Department of Physics and Astronomy Glasgow University, Glasgow G12 8QQ, Scotland and H. B. Nielsen Niels
More informationFundamental Physics: Quantum Field Theory
Mobolaji Williams (mwilliams@physics.harvard.edu x) First Version: June 1, 216 Fundamental Physics: Quantum Field Theory What is the topic? Quantum field theory refers to the quantum theory of fields in
More informationLecture 39, 40 Supplement: Particle physics in the LHC era
Lecture 39, 40 Supplement: Particle physics in the LHC era The Matter Particles (Fermions) plus their antiparticles... What is measured? quarks confined into hadrons A zoo of strongly interacting particles...
More informationMajorana and Majorana Fermions. From Romance to Reality
Majorana and Majorana Fermions From Romance to Reality The Romance of Ettore Majorana (19061938?) There are many categories of scientists: People of second and third rank, who do their best, but do not
More informationBeta functions in quantum electrodynamics
Beta functions in quantum electrodynamics based on S66 Let s calculate the beta function in QED: the dictionary: Note! following the usual procedure: we find: or equivalently: For a theory with N Dirac
More informationReview Chap. 18: Particle Physics
Final Exam: Sat. Dec. 18, 2:454:45 pm, 1300 Sterling Exam is cumulative, covering all material Review Chap. 18: Particle Physics Particles and fields: a new picture Quarks and leptons: the particle zoo
More informationSymmetries and Group Theory  Lecture 2
Symmetries and Group Theory  Lecture 2 1 Introduction Physics attempts to look for the global aspects of a system, since much of system behavior can be understood from general principles without investigating
More informationPhoton Coupling with Matter, u R
1 / 16 Photon Coupling with Matter, u R Consider the up quark. We know that the u R has electric charge 2 3 e (where e is the proton charge), and that the photon A is a linear combination of the B and
More informationPARTICLE PHYSICS COLUMBIA SCIENCE HONORS PROGRAM WEEK 7 OVERVIEW OF THE STANDARD MODEL (CONT ED) LIMITATIONS OF THE STANDARD MODEL
PARTICLE PHYSICS COLUMBIA SCIENCE HONORS PROGRAM WEEK 7 OVERVIEW OF THE STANDARD MODEL (CONT ED) LIMITATIONS OF THE STANDARD MODEL COURSE POLICIES Attendance Up to four excused absences Two with notes
More informationSM predicts massless neutrinos
MASSIVE NEUTRINOS SM predicts massless neutrinos What is the motivation for considering neutrino masses? Is the question of the existence of neutrino masses an isolated one, or is connected to other outstanding
More informationPAPER 305 THE STANDARD MODEL
MATHEMATICAL TRIPOS Part III Tuesday, 6 June, 017 9:00 am to 1:00 pm PAPER 305 THE STANDARD MODEL Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight.
More informationNeutrino Physics. KamBiu Luk. Tsinghua University and University of California, Berkeley and Lawrence Berkeley National Laboratory
Neutrino Physics KamBiu Luk Tsinghua University and University of California, Berkeley and Lawrence Berkeley National Laboratory 415 June, 2007 Outline Brief overview of particle physics Properties of
More informationThe ATLAS detector at the Large Hadron Collider: to boldly look where no one has looked before
The ATLAS detector at the Large adron Collider: to boldly look where no one has looked before UBC 14 July 2006 Michel Lefebvre Physics and Astronomy University of Victoria The ATLAS detector at the Large
More informationChapter 10 Operators of the scalar Klein Gordon field. from my book: Understanding Relativistic Quantum Field Theory.
Chapter 10 Operators of the scalar Klein Gordon field from my book: Understanding Relativistic Quantum Field Theory Hans de Vries November 11, 2008 2 Chapter Contents 10 Operators of the scalar Klein Gordon
More informationParticle Physics. Lecture 11: Mesons and Baryons
Particle Physics Lecture 11: Mesons and Baryons Measuring Jets Fragmentation Mesons and Baryons Isospin and hypercharge SU(3) flavour symmetry Heavy Quark states 1 From Tuesday: Summary In QCD, the coupling
More informationParticle Physics Outline the concepts of particle production and annihilation and apply the conservation laws to these processes.
Particle Physics 12.3.1 Outline the concept of antiparticles and give examples 12.3.2 Outline the concepts of particle production and annihilation and apply the conservation laws to these processes. Every
More informationLarge Hadron Collider
Large Hadron Collider Himadri Barman TSU, JNCASR September 18, 2008 00 Large Hadron Collider (LHC): Plan We ll see 4 short videos. In between I ll give you a little guideline. Purpose is to understand
More informationBig Bang Planck Era. This theory: cosmological model of the universe that is best supported by several aspects of scientific evidence and observation
Big Bang Planck Era Source: http://www.crystalinks.com/bigbang.html Source: http://www.odec.ca/index.htm This theory: cosmological model of the universe that is best supported by several aspects of scientific
More informationPHYS 3446 Lecture #21
PHYS 3446 Lecture #21 Monday, Nov. 27, 2006 Dr. 1. The Standard Model Quarks and Leptons Gauge Bosons Symmetry Breaking and the Higgs particle Higgs Search Strategy Issues in the Standard Model Neutrino
More informationSpectral Triples and Supersymmetry
Ma148b Spring 2016 Topics in Mathematical Physics Reference: Wim Beenakker, Thijs van den Broek, Walter van Suijlekom, Supersymmetry and Noncommutative Geometry, Springer, 2015 (also all images in this
More informationSuperfluidity and Symmetry Breaking. An Unfinished Symphony
Superfluidity and Symmetry Breaking An Unfinished Symphony The Classics The simplest model for superfluidity involves a complex scalar field that supports a phase (U(1)) symmetry in its fundamental equations,
More informationLecture notes for FYS610 Many particle Quantum Mechanics
UNIVERSITETET I STAVANGER Institutt for matematikk og naturvitenskap Lecture notes for FYS610 Many particle Quantum Mechanics Note 20, 19.4 2017 Additions and comments to Quantum Field Theory and the Standard
More informationYANGMILLS THEORY. This theory will be invariant under the following U(1) phase transformations
YANGMILLS THEORY TOMAS HÄLLGREN Abstract. We give a short introduction to classical YangMills theory. Starting from Abelian symmetries we motivate the transformation laws, the covariant derivative and
More informationTHE INSTITUTE FOR SCIENTIFIC COMPUTING AND APPLIED MATHEMATICS
Color Algebra in Quantum Chromodynamics Tian Ma and Shouhong Wang December 30,2013 Preprint No.: 1401 THE INSTITUTE FOR SCIENTIFIC COMPUTING AND APPLIED MATHEMATICS INDIANA UNIVERSITY COLOR ALGEBRA IN
More informationElectroweak physics and the LHC an introduction to the Standard Model
Electroweak physics and the LHC an introduction to the Standard Model Paolo Gambino INFN Torino LHC School Martignano 1218 June 2006 Outline Prologue on weak interactions Express review of gauge theories
More informationE 6 Spectra at the TeV Scale
E 6 Spectra at the TeV Scale InstitutsSeminar Kerne und Teilchen, TU Dresden Alexander Knochel Uni Freiburg 24.06.2010 Based on: F. Braam, AK, J. Reuter, arxiv:1001.4074 [hepph], JHEP06(2010)013 Outline
More information32 IONIZING RADIATION, NUCLEAR ENERGY, AND ELEMENTARY PARTICLES
32 IONIZING RADIATION, NUCLEAR ENERGY, AND ELEMENTARY PARTICLES 32.1 Biological Effects of Ionizing Radiation γrays (highenergy photons) can penetrate almost anything, but do comparatively little damage.
More information3. Introductory Nuclear Physics 1; The Liquid Drop Model
3. Introductory Nuclear Physics 1; The Liquid Drop Model Each nucleus is a bound collection of N neutrons and Z protons. The mass number is A = N + Z, the atomic number is Z and the nucleus is written
More informationTheoretical High Energy Physics in the LHC Era
Theoretical High Energy Physics in the LHC Era Talk to Physics 205, Jan. 2013 Department of Physics and Santa Cruz Institute for Particle Physics University of California, Santa Cruz January, 2013 We have
More informationGrand Unified Theories and Supersymmetry in Particle Physics and Cosmology
IEKPKA/9401 hepph/9402266 March, 1994 arxiv:hepph/9402266v5 7 Feb 2001 Grand Unified Theories and Supersymmetry in Particle Physics and Cosmology W. de Boer 1 Inst. für Experimentelle Kernphysik, Universität
More informationBosons in the Zoo of Elementary Particles
Bosons in the Zoo of Elementary Particles Daniele Sasso * Abstract In this paper we want to raise the question concerning the physical identity of bosons and the function that they perform in the NonStandard
More informationSUSY Phenomenology & Experimental searches
SUSY Phenomenology & Experimental searches Slides available at: Alex Tapper http://www.hep.ph.ic.ac.uk/~tapper/lecture.html Objectives  Know what Supersymmetry (SUSY) is  Understand qualitatively the
More informationMasses and the Higgs Mechanism
Chapter 8 Masses and the Higgs Mechanism The Z, like the W ± must be very heavy. This much can be inferred immediately because a massless Z boson would give rise to a peculiar parityviolating longrange
More informationAn overview of SU(5) grand unification. Nicola Canzano. Physics Dept. University of California, Santa Cruz. March 2016
Physics Dept. University of California, Santa Cruz March 2016 A Quick Review of the Standard Model (1) In 1954, C.N. Yang and Robert Mills gave us the tools necessary to build quantum field theories out
More informationThe KleinGordon equation
Lecture 8 The KleinGordon equation WS2010/11: Introduction to Nuclear and Particle Physics The bosons in field theory Bosons with spin 0 scalar (or pseudoscalar) meson fields canonical field quantization
More informationEffective Field Theory for Charge Carriers in an Antiferromagnet
Effective Field Theory for Charge Carriers in an Antiferromagnet Diplomarbeit der Philosophischnaturwissenschaftlichen Fakultät der Universität Bern vorgelegt von Florian Kämpfer März 2005 Leiter der
More informationPhysics 129, Fall 2010; Prof. D. Budker
Physics 129, Fall 2010; Prof. D. Budker Some introductory thoughts Reductionists science Identical particles are truly so (bosons, fermions) We will be using (relativistic) QM where initial conditions
More informationUnified Field Equations Coupling Four Forces and Theory of Dark Matter and Dark Energy
Unified Field Equations Coupling Four Forces and Theory of Dark Matter and Dark Energy Tian Ma, Shouhong Wang Supported in part by NSF and ONR http://www.indiana.edu/ fluid 1 Outline I. Motivations II.
More informationRepresentations of Lorentz Group
Representations of Lorentz Group based on S33 We defined a unitary operator that implemented a Lorentz transformation on a scalar field: How do we find the smallest (irreducible) representations of the
More informationParticle physics: what is the world made of?
Particle physics: what is the world made of? From our experience from chemistry has told us about: Name Mass (kg) Mass (atomic mass units) Decreasing mass Neutron Proton Electron Previous lecture on stellar
More informationThe Quark Parton Model
The Quark Parton Model Quark Model Pseudoscalar J P = 0 Mesons Vector J P = 1 Mesons Meson Masses J P = 3 /2 + Baryons J P = ½ + Baryons Resonances Resonance Detection Discovery of the ω meson Dalitz Plots
More information7 Quantized Free Dirac Fields
7 Quantized Free Dirac Fields 7.1 The Dirac Equation and Quantum Field Theory The Dirac equation is a relativistic wave equation which describes the quantum dynamics of spinors. We will see in this section
More informationPHY 396 K. Problem set #11, the last set this semester! Due December 1, 2016.
PHY 396 K. Problem set #11, the last set this semester! Due December 1, 2016. In my notations, the A µ and their components A a µ are the canonically normalized vector fields, while the A µ = ga µ and
More informationMinimal Supersymmetric Standard Model (MSSM). Nausheen R. Shah
Minimal Supersymmetric Standard Model (MSSM). Nausheen R. Shah June 8, 2003 1 Introduction Even though the Standard Model has had years of experimental success, it has been known for a long time that it
More informationThe Role and Discovery of the Higgs
The Role and Discovery of the Higgs David Clarke Abstract This paper summarizes the importance of the Higgs boson in QFT and outlines experiments leading up to the discovery of the Higgs boson. First we
More informationBACKGROUND LHC Physics Program Summary LHC PHYSICS. Andrés G. Delannoy 1. 1 Vanderbilt University. 2014/07/21 1
2014/07/21 delannoy@cern.ch 1 LHC PHYSICS Andrés G. Delannoy 1 1 Vanderbilt University 2014/07/21 delannoy@cern.ch 2 1 BACKGROUND The Large Hadron Collider The Standard Model The Higgs Mechanism SuperSymmetry
More informationMaxwell s equations. based on S54. electric field charge density. current density
Maxwell s equations based on S54 Our next task is to find a quantum field theory description of spin1 particles, e.g. photons. Classical electrodynamics is governed by Maxwell s equations: electric field
More informationEvidence for the Strong Interaction
Evidence for the Strong Interaction Scott Wilbur Scott Wilbur Evidence for the Strong Interaction 1 Overview Continuing search inside fundamental particles Scott Wilbur Evidence for the Strong Interaction
More informationElementary particles, forces and Feynman diagrams
Elementary particles, forces and Feynman diagrams Particles & Forces quarks Charged leptons (e,µ,τ) Neutral leptons (ν) Strong Y N N Electro Magnetic Y Y N Weak Y Y Y Quarks carry strong, weak & EM charge!!!!!
More informationFrom Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics: measurements and uncertainty Smashing things together: from Rutherford to the LHC Particle Interactions Quarks
More informationThe ATLAS Experiment and the CERN Large Hadron Collider
The ATLAS Experiment and the CERN Large Hadron Collider HEP1012 April 5, 2010 A. T. Goshaw Duke University 1 HEP 101 Plan March 29: Introduction and basic HEP terminology March 30: Special LHC event:
More informationNTNU Trondheim, Institutt for fysikk
NTNU Trondheim, Institutt for fysikk Examination for FY3464 Quantum Field Theory I Contact: Michael Kachelrieß, tel. 998971 Allowed tools: mathematical tables 1. Spin zero. Consider a real, scalar field
More information