Special Relativity and Quantum Theory : A Collection of Papers on the Poincaré Group

Special relativity and quantum mechanics are likely to remain the two most important languages in physics for many years to come. The underlying language for both disciplines is group theory. Eugene P. Wigner's 1939 paper on the Unitary Representations of the Inhomogeneous Lorentz Group laid the foundation for unifying the concepts and algorithms of quantum mechanics and special relativity. In view of the strong current interest in the space-time symmetries of elementary particles, it is safe to say that Wigner's 1939 paper was fifty years ahead of its time. This edited volume consists of Wigner's 1939 paper and the major papers on the Lorentz group published since 1939. . This volume is intended for graduate and advanced undergraduate students in physics and mathematics, as well as mature physicists wishing to understand the more fundamental aspects of physics than are available from the fashion-oriented theoretical models which come and go. The original papers contained in this volume are useful as supplementary reading material for students in courses on group theory, relativistic quantum mechanics and quantum field theory, relativistic electrodynamics, general relativity, and elementary particle physics. This reprint collection is an extension of the textbook by the present editors entitled "Theory and Applications of the Poincare Group." Since this book is largely based on the articles contained herein, the present volume should be viewed as a reading for the previous work. continuation of and supplementary We would like to thank Professors J. Bjorken, R. Feynman, R. Hofstadter, J.

I: Perspective View of Quantum Space-Time Symmetries.- 1. Relativistic Invariance and Quantum Phenomena, Rev. Mod. Phys, 29, 255 (1957).- 2. The Early Years of Relativity, in Albert Einstein: Historical and Cultural Perspectives: The Centennial Symposium in Jerusalem, edited by G. Holton and Y. Elkana (Princeton Univ. Press, Princeton, New Jersey, 1979).- II: Representations of the Poincaré Group.- 1. On Unitary Representations of the Inhomogeneous Lorentz Group, Ann. Math. 40, 149 (1939)..- 2. Group Theoretical Discussion of Relativistic Wave Equations, Proc. Nat. Acad. Sci. (U.S.A.) 34, 211 (1948).- 3. Unitary Representations of the Lorentz Group, Proc. Roy. Soc. (London)Al83, 284 (1945).- 4. Feynman Rules for Any Spin, Phys. Rev. 133, B1318 (1964).- 5. Representations of the Poincaré Group for Relativistic Extended Hadrons, J. Math. Phys. 20, 1341 (1979).- 6. A Simple Method for Illustrating the Difference between the Homogeneous and Inhomogeneous Lorentz Groups, Am. J. Phys. 47, 892 (1979).- III: The Time-Energy Uncertainty Relation.- 1. The Quantum Theory of the Emission and Absorption of Radiation, Proc. Roy. Soc. (London) A114, 243 (1927).- 2. The Quantum Theory of Dispersion, Proc. Roy. Soc. (London) A114, 710 (1927).- 3. On the Time-Energy Uncertainty Relation, in Aspects of Quantum Theory, in Honour of P. A. M. Dirac’s 70th Birthday, edited by A. Salam and E. P. Wigner (Cambridge Univ. Press, London, 1972).- 4. Time-Energy Uncertainty Relation and Lorentz Covariance, Am. J. Phys. 53, 142 (1985).- IV: Covariant Picture of Quantum Bound States.- 1. Forms of Relativistic Dynamics, Rev. Mod. Phys. 27, 392 (1949).- 2. Quantum Theory of Non-Local Fields. Part I. Free Fields, Phys. Rev. 77, 219 (1950).- 3. Quantum Theory of Non-Local Fields. Part II. Irreducible Fields and Their Interaction, Phys. Rev. 80, 1047 (1950).- 4. Structure and Mass Spectrum of Elementary Particles. I. General Considerations, Phys. Rev. 91, 415 (1953).- 5. Structure and Mass Spectrum of Elementary Particles. II. Oscillator Model, Phys. Rev. 91, 416 (1953).- 6. Properties of the Bethe-Salpeter Wave Functions, Phys. Rev. 96, 1124 (1954).- 7. Covariant Harmonic Oscillators and the Quark Model, Phys. Rev. D 8, 3521 (1973).- 8. Orthogonality Relation for Covariant Harmonic- Oscillator Wave Functions, Phys. Rev. D 10, 4306 (1974).- 9. Complete Orthogonality Relations for the Covariant Harmonic Oscillator, Phys. Rev. D 23, 3078 (1981).- 10. Dirac’s Form of Relativistic Quantum Mechanics, Am. J. Phys. 49, 1157 (1981).- V: Lorentz-Dirac Deformation in High Energy Physics.- 1. Electron Scattering from the Proton, Phys. Rev. 98, 183 (1955).- 2. Nucleon Electromagnetic Form Factors at High Momentum Transfers in an Extended Particle Model based on the Quark Model, Prog. Theor. Phys. 43, 73 (1970).- 3. The Behavior of Hadron Collisions at Extreme Energies in High Energy Collisions, Proceedings of the Third International Conference, Stony Brook, New York, edited by C. N. Yang et al. (Gordon and Breach, New York, 1969).- 4. Inelastic Electron-Proton and ?- Proton Scattering and the Structure of the Nucleon, Phys. Rev. 185, 1975 (1969).- 5. Covariant Harmonic Oscillators and the Parton Picture, Phys. Rev. D 15, 335 (1977).- 6. Valons and Harmonic Oscillators, Phys. Rev. D 23, 2781 (1981).- VI: Massless Particles and Gauge Transformations.- 1. Feynman Rules for Any Spin II. Massless Particles, Phys. Rev. 134, B882 (1964).- 2. Photons and Gravitons in S-Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass, Phys. Rev. 135, B1049 (1964).- 3. E(2)-Like Little Group for Massless Particles and Neutrino Polarization as a Consequence of Gauge Invariance, Phys. Rev. D 26, 3717 (1982).- VII: Group Contractions.- 1. On the Contraction of Groups and Their Representations, Proc. Nat. Acad. Sci. (U.S.A.) 39, 510 (1953).- 2. Internal Space-Time Symmetries of Massive and Massless Particles, Am. J. Phys. 52, 1037 (1984).- 3. Eulerian Parametrization of Wigner’s Little Groups and Gauge Transformations in Terms of Rotations in Two-Component Spinors, J. Math. Phys. 27, 2228 (1986).- 4. Cylindrical Group and Massless Particles, J. Math. Phys. 28, 1175 (1987).- VIII: Localization Problems.- 1. Localized States for Elementary Systems, Rev. Mod. Phys. 21, 400 (1949).- 2. On the Localizability of Quantum Mechanical Systems, Rev. Mod. Phys. 34, 845 (1962).- 3. Uncertainty Relations for Light Waves and the Concept of Photons, Phys. Rev. A 35, 1682 (1987).- IX: Lorentz Transformations.- 1. Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field, Phys. Rev. Lett. 2, 435 (1959).- 2. Is There a Link Between Gauge Invariance, Relativistic Invariance, and Electron Spin?, Nuovo Cimento 3IB, 1 (1976).- 3. Special Relativity and Diagonal Transformations, Am. J. Phys. 38, 218 (1970).- 4. A Useful Form of the Minkowski Diagram, Am. J. Phys. 38, 1298 (1970).- 5. SU(2) and SU(1,1) Interferometers, Phys. Rev. A 33, 4033 (1986).- 6. Thomas Precession, Wigner Rotations and Gauge Transformations, Class. Quantum Grav. 4, 1777 (1987).- 7. Linear Canonical Transformations of Coherent and Squeezed States in the Wigner Phase Space, Phys. Rev. A 37, 807 (1988).