Pauli and the spin-statistics theorem

526 Pages·1998·34.581 MB·English

by  Duck, Ian, Sudarshan, Ennackel Chandy George

Pauli and the
Spin-Statistics Theorem
This page is intentionally left blank
Ian Duck
Rice University, Houston, Texas, USA
E C G Sudarshan
University of Texas at Austin, USA
Pauli and the
Spin-Statistics Theorem
World Scientific
lb Singapore • New Jersey • London • Hong Kong
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World Scientific Publishing Co. Pte. Ltd.
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Library of Congress Cataloging-in-Publication Data
Pauli and the spin-statistics theorem / editors, Ian Duck, E.C.G. Sudarshan.
p. cm.
Includes bibliographical references and index.
ISBN 9810231148
1. Nuclear spin - Mathematical models. 2. Nuclear spin - Statistical methods.
3. Pauli exclusion principle. I. Duck, Jan. 1933-
II. Sudarshan, E. C. G.
QC793.3.S6P38 1997
530.13'3-dc21 97-36353
CIP
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
First published 1997
First reprint 1998
Copyright © 1997 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. Thisbook, or parts thereof, may not be reproducedin any form or by any means, electronic
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Printed in Singapore.
Table of Contents
AUTHORS - page IX.
ACKNOWLEDGEMENTS - page X.
FOREWORD - page 1-20. §0.1: Introduction; §0.2: Preliminary Remarks; §0.3: Anti-
commutation Relations for Dirac Spin-| fields; §0.4: Commutation Relations for Klein-Gordon
Fields; §0.5: Concluding Remarks; Bibliography and References.
Part I: The Historic Era
CHAPTER 1 - Discovery of the Exclusion Principle - page 21-49. §1.1: Introduction;
§1.2: Pauli's Deduction of the Exclusion Principle; §1.3: Stoner's Explanation of the
Periodic Table; §1.4: Biographical Note on E.C. Stoner; Bibliography and References;
Appendix 1A: from W. Pauli, Zeits. f. Phys. 31, 765 (1925); Appendix IB: from E.C.
Stoner, Phil. Mag. 48, 719 (1924).
CHAPTER 2 - The Discovery of the Electron Spin-| - page 50-71. §2.1: Introduction;
§2.2: Goudsmit and Uhlenbeck's Discovery of Spin; §2.3: Kronig's Frustrated Discovery
of the Electron Spin; §2.4: Biographical Notes on: A.H. Compton, S.A. Goudsmit, G.E.
Uhlenbeck, and R.deL. Kronig; Bibliography and References; Appendix 2A: from G.E.
Uhlenbeck and S.A. Goudsmit, Die Naturwissenschaften 47, 953 (1925); Appendix 2B:
from G.E. Uhlenbeck and S.A. Goudsmit, Nature 117, 264 (1926); Appendix 2C: from
A.H. Compton, Journal of the Franklin Institute 192, 145 (1921); Appendix 2D: from
R.deL. Kronig, Nature 117, 550 (1926).
CHAPTER 3 - Bose-Einstein Statistics -page 72-107. §3.1: Bose's Quantum Deriva­
tion of Planck's Distribution; §3.2: Einstein's Application of Bose's New Insight; §3.3:
Biographical Note on S.N. Bose; Bibliography and References; Appendix 3A: from Bose,
Zeits. f. Phys. 26, 178 (1924); Appendix 3B,C,D: from A. Einstein, S.B.d. Preuss. Akad.
Wiss. Ber. 22, 261 (1924); 1, 3 (1925); 3, 18 (1925).
CHAPTER 4 - Wave Function of States of Many Identical Particles - page 108-130.
§4.1: Introduction; §4.2: Heisenberg's Deduction of the Symmetrization Requirement;
§4.3: Dirac's Introduction of the Symmetrization Postulate; §4.4: Epilog; §4.5: Biographi­
cal Note on Heisenberg; Bibliography and References; Appendix 4A: from W. Heisenberg,
Zeits. f. Phys. 38, 411 (1926); from P.A.M. Dirac, Proc. Roy. Soc. A112, 661 (1926).
CHAPTER 5 - Fermi-Dirac Statistics - page 131-148. §5.1: Introduction to Fermi's
Derivation; §5.2: Dirac's Derivation of Fermi-Dirac Statistics; §5.3: Biographical Note on
V
Enrico Fermi; Bibliography and References; Appendix 5A: from E. Fermi, Zeits. f. Phys.
36, 902 (1926); Appendix 5B: from P.A.M. Dirac, Proc. Roy. Soc. A112, 661 (1926).
CHAPTER 6 - Dirac's Invention of Quantum Field Theory - page 149-167. §6.1:
Introductory Remarks; §6.2: Dirac's Invention of Second Quantization; §6.3: Application
to Photon Emission and Absorption; Bibliography and References; Appendix 6A: from
P.A.M. Dirac, Proc. Roy. Soc. A114, 243 (1927).
CHAPTER 7 - The Jordan-Wigner Invention of Anticommutation for Fermi-Dirac
Fields-page 168-203. §7.1: Introduction; §7.2: Jordan's Introduction of Anticommutation
Relations; §7.3: Jordan and Wigner's Algebraic Developments; §7.4: Biographical Note
on E.P. Jordan; Bibliography and References; Appendix 7A: from P. Jordan, Zeits. f.
Phys. 44, 473 (1927); Appendix 7B: from P. Jordan and E. Wigner, Zeits. f. Phys. 47,
631 (1928).
CHAPTER 8 - From Hole Theory to Positrons - page 204-228. §8.1: The Dirac Equa­
tion; §8.2: The Reinterpretation of Holes as Antiparticles; §8.3: Feynman's Interpretation
of Dirac's Scenario; §8.4: Biographical Note on Dirac; Bibliography and References; Ap­
pendix 8A: from P.A.M. Dirac, Proc. Roy. Soc. A117, 610 (1928); Appendix 8B: from
P.A.M. Dirac, Proc. Roy. Soc. A126, 360 (1930); Appendix 8C: from J.R. Oppenheimer,
Phys. Rev. 35, 562 (1930); Appendix 8D: from H. Weyl, The Theory of Groups and
Quantum Mechanics (Dover, New York, 1930); Appendix 8E: from P.A.M. Dirac, Proc.
Roy. Soc. A133, 60 (1931); Appendix 8F: from CD. Anderson, Phys. Rev. 43, 491
(1933).
CHAPTER 9 - Canonical Quantization of the Klein-Gordon Field - page 229-255.
§9.1: Introduction; §9.2: Review of Lagrangian and Hamiltonian Classical Mechanics;
§9.3: Canonical Quantization, First and Second Quantization; §9.4: Quantization of the
Klein-Gordon Field; §9.5: Biographical Note on Weisskopf; Bibliography and References;
Appendix 9A: from W. Pauli and V. Weisskopf, Helv. Phys. Acta 7, 709 (1934).
Part II: The Pauli Era
CHAPTER 10 - Pauli's First Proof of the Spin-Statistics Theorem - page 256-276.
§10.1: Pauli's First Proof; §10.2: Iwanenko and Socolow's Second Quantization of the
Dirac Equation; §10.3: Biographical Note on Iwanenko and Socolow; Bibliography and
References; Appendix 10A: from W. Pauli, Ann. Inst H. Poincare 6, 137 (1936); Appendix
10.B: D. Iwanenko and A. Socolow, Phys. Zeits. d. Sowjetunion 11, 590 (1937).
VI
CHAPTER 11 - Fierz's Proof of the Spin-Statistics Theorem - page 277-300. §11.1:
Introduction; §11.2: Guide to Fierz's Proof: Integral Spin; §11.3: Guide to Fierz's Proof;
Half-Integral Spin; §11.4: Concluding Remarks; §11.5: Biographical Note on Fierz; Bibli­
ography and References; Appendix 11A: from M. Fierz, Helv. Phys. Acta 12, 3 (1939).
CHAPTER 12 - Belinfante's Proof of the Spin-Statistics Theorem - page 301-329.
§12.1: Introduction; §12.2: Belinfante's Proof using Charge-Conjugation; §12.3: Pauli's
Criticism; §12.4: Concluding Remarks; §12.5: Biographical Note on F.J. Belinfante; Bib­
liography and References; Appendix 12A: from F.J. Belinfante, Physica 6, 870 (1939);
Appendix 12B: from W. Pauli and F.J. Belinfante, Physica 7, 177 (1940).
CHAPTER 13 - deWet's Proof Based on Canonical Field Theory - page 330-344.
§13.1: Introduction; §13.2: deWet's Proof of the Spin-Statistics Theorem; §13.3: Bio­
graphical Note on J.S. deWet; Bibliography and References; Appendix 13A: from J.S. de
Wet, PhD Thesis, Princeton Mathematics, 1939; Appendix 13B: J.S. deWet, Phys. Rev.
57, 646 (1940).
CHAPTER 14 - Pauli's Proof of the Spin-Statistics Theorem - page 345-366. §14.1:
Introduction; §14.2: Outline of Pauli's Proof; §14.3: Guide to Pauli's Proof; §14.4: Sum­
mary of Pauli's Proof; §14.5: Comparison of Fierz and Pauli Proofs; §14.6: Biographical
Note on Pauli; Bibliography and References; Appendix 14A: from W. Pauli, Phys. Rev.
58, 716 (1940).
Part III: The Wightman-Schwinger Era
CHAPTER 15 - Feynman's Proof and Pauli's Criticism - page 368-389. §15.1: In­
troduction; §15.2: Feynman's Calculation of Vacuum Polarization; §15.3: Pauli's Analysis
of Feynman's Proof; §15.4: Concluding Remarks; §15.5 Biographical Note on Feynman;
Bibliography and References; Appendix 15A: from R.P. Feynman, Phys. Rev. 76, 749
(1949); Appendix 15B: from R.P. Feynman, Phys. Rev. 76, 769 (1949); Appendix 15C:
from W. Pauli, Progr. Theor. Phys. 5, 526 (1950).
CHAPTER 16 - Schwinger's Proof Using Time Reversal Invariance - page 390-404.
§16.1: Introduction; §16.2: Schwinger's Proof. §16.3: Concluding Remarks; §16.4: Bi­
ographical Note on Schwinger; Bibliography and References; Appendix 16A: from J.
Schwinger, Phys. Rev. 82, 914 (1951).
CHAPTER 17 - The Proofs of Liiders and Zumino, and of Burgoyne - page 405-424.
VII
§17.1: Introduction. The Luders and Zumino Proof; §17.2: Burgoyne's Proof of the Spin-
Statistics Theorem; §17.3: Concluding Remarks; §17.4: Biographical Notes on Luders,
Zumino, and Burgoyne; Bibliography and References; Appendix 17A: from G. Luders and
B. Zumino, Phys. Rev. 110, 1450 (1958); Appendix 17B: from N. Burgoyne, Nuovo Cim.
8, 607 (1958).
CHAPTER 18 - The Hall-Wightman Theorem - page 425-447. §18.1: Introduction.
Analytic Continuation for Free Fields; §18.2: The Essential Result of the Hall-Wightman
Theorem; §18.3: Jost's Summary of the Pauli Era; §18.4: Biographical Note on Wightman;
§18.5: Biographical Note on Jost; Bibliography and References; Appendix 18A: from A.S.
Wightman, Phys. Rev. 101, 860 (1956); Appendix 18B: from D. Hall and A.S. Wightman,
Mat. Fys. Medd. Dan. Vid. Selsk. 31, 5 (1957); Appendix 18C: from R. Jost, in
Theoretical Physics in the Twentieth Century: A Memorial Volume to Wolfgang Pauli
(Interscience, New York, 1960).
CHAPTER 19 - Schwinger, Euclidean Field Theory, Source Theory, and the Spin-
Statistics Connection - page 448-463. §19.1: Introduction; §19.2: Euclidean Field Theory;
§19.3: Euclidean Proof of the Spin-Statistics Theorem; §19.4: Schwinger's Source Theory;
§19.5: Concluding Remarks; Bibliography and References.
Part IV: The Contemporary Era
CHAPTER 20 - Responses to Neuenschwander's Question. Evaluation of Intuitive
Proofs of the Spin-Statistics Theorem - page 464-484. §20.1: Introduction; §20.2: Bacry's
Proof and Hilborn's Critique; §20.3: Topological Markers and Feynman's Models; §20.4:
Critique of Topological Markers; §20.4: Feynman's Unitarity Argument Revisited; Bibli­
ography and References.
CHAPTER 21 - Overview and Epilog - page 485-503. §21.1: Introduction; §21.2:
Elementary Proof of the Spin-Statistics Theorem; §21.3: Further Comment on the Ele­
mentary Proof; §21.4: Dirac Equation from Grassmann Theory; §21.5: No Bose-Einstein
Dirac Action; §21.6: No Fermi-Dirac Klein-Gordon Action; §21.7: Concluding Remarks;
§21.8: Final Summary; Bibliography and References.
Index - page 505.
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Authors
Ian Duck, b. 1933 Kamloops, Canada; BSc 55 Queen's; res asst, 55-
56 UBC; PhD 61 Caltech; Research Assoc. 61-63 USC; Research Assoc.
to Prof of Physics 63- Rice University; theoretical research in nuclear and
particle physics from ev to Gev; radiative capture of light nuclei, muon
capture, bremstrahlung in p-p scattering, Faddeev equations, N-A process,
quark model of nucleon structure, models of color confinement, quark-gluon
plasma excitation in 10 Gev p-nucleus annihilation, fine structure of the
baryon octet-decuplet spectrum.
Ennackel Chandy George Sudarshan, b. 1931 Kottayam, India;
BSc 51, MA 52 Madras; res asst 52-55 Tata Inst; PhD 58 Rochester; Res
Fellow 57-59 Harvard; to Assoc Prof Rochester 59-64; Prof Syracuse 64-69;
Prof of Physics, Center for Theoretical Physics, Texas 69- ; concurrent po­
sitions at Bern 63-64, Brandeis 64, Madras 70-71, Bangalore 72-. Honors:
DSc from Wisconsin, Delhi, Chalmers, Madras, Burdwan, Cochin; Medals:
Order of the Lotus, Bose Medal, Sarvadhikari Medal and many others. Re­
search accomplishments: coinventer with R.E. Marshak of the universal V-A
weak interaction (1957); published six books and over 350 journal articles in
the areas of elementary particle theory, quantum theory, group theory, quan­
tum optics, and the foundations, philosophy and history of contemporary
physics.
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