Lecture Notes in Physics
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1 Lecture Notes in Physics Edited by H. Araki, Kyoto, J. Ehlers, MLinchen, K. Hepp, ZUrich R. Kippenhahn, MLinchen, H.A. WeidenmSIler, Heidelberg J. Wess, Karlsruhe and J. Zittartz, KSIn Managing Editor: W. Beiglb6ck 308 Henri Bacry Localizability and Space in Quantum Physics Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo
2 Author Henri Bacry Centre de Physique Th~orique, C.N.R.S., Case 90? F Marseille, Cedex 9, France ISBN Springer-Verlag Berlin Heidelberg NewYork ISBN 0-38? Springer-Verlag NewYork Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. Springer-Verlag Berlin Heidelberg 1988 Printed in Germany Printing: Druckhaus Beltz, Hemsbach/Bergetr. Binding: J. Sch~ffer GmbH & Co. KG., Gr0nstadt
3 To Yael H_~l~ne Jacques-Daniel Emmanuel
4 SUMMARY. Introduction Historical sketch on the nature of light The correspondence principle, the wave corpuscle duality, the complementarity principle and the slit experiment The spin quantization problem l_x)calizability. The photon scandal. Quantization helpless! A position operator for the photon. Giving up the complementary principle Departing from the Newton-Wigner-Wightman axioms Is Minkowski space-time suitable for particle physics? 53 Appendix A. The symplectic structure of coadjoint orbks. 61 Appendix B. The quantization of the sphere S Appendix C. The angular momentum of an electric charge in the monopole field (an application of the Noether theorem). 64 Appendix D. Non localizability of the classical massless particle with helicity. 66 Appendix E.The Maxwell equations and the Poincar6 group. 70 Appendix F. The zitterbewegung. The Pryce-Foldy-Wouthuysen transformation. 75 Quotations. 79 Index of Names. 80
5 ACKNOWLEDGMENTS I am grateful to Professor Louis Michel for his hospitality at the lnstitut des Hautes Etudes Scientifiques at Bures-sur-Yvette, where this work started. Part of the actual writing was done at the International Centre for Theoretical Physics in Trieste, for which I am indebted to Professor Abdus Salam. I must also thank Professors L.C. Biedenharn (Durham), L.N. Chang (Blacksburg), N.P. Chang (New York), L.P. Horwitz and Y. Ne'eman (Tel-Aviv), J. Patera (Montrdal) and J. Zak (Haifa), who gave me the opportunity to give talks on the subject and to have stimulating discussions with various people. Many thanks are due to those who followed or helped my efforts in writing the present work, namely A.J. Bracken, D. Kastler, L. Michel, J. Zak and especially to L.C. Biedenharn and A. Grossmann, who also read and criticized the preliminary text. I owe a particular debt of gratitude to A. Connes. This work would never have been written without his enthusiasm in the enlightening discussions we had.
6 "Ce serait pourtant de l'optimisme exagdrd de croire que le moment analytique soit disparu et ddfinitivement remplacd par la synthdse. II est encore loin de sa disparition et ne fait qu'emp~cher le d~veloppement de la racine synthdtique". Vassily Kandinsky, XX e sidcle, 3 (1938).
Lecture Notes in Physics
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