Toward an understanding of the spin-statistics theorem

American Journal of Physics

Volumn 66, Issue 4, 1998, Pages 284-303

  Duck, Ian ^a   Sudarshan, E C G ^b  

^a RICE UNIVERSITY   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032381104     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18860     Document Type: Article

References (79)

1. D. E. Neuenschwander, "Question #7. The spin-statistics theorem," Am. J. Phys. 62 (11), 972 (1994).
2. W. Pauli, "The Connection Between Spin and Statistics," Phys. Rev. 58, 716-722 (1940).
3. R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That (Benjamin, New York, 1964), pp. 96, 146.
4. R. C. Hilborn, "Answer to Question #7 ['The spin-statistics theorem,' D. E. Neuenschwander]," Am. J. Phys. 63 (4), 298-299 (1995).
5. J. Schwinger, "Spin, Statistics and the TCP Theorem, and Addendum," Proc. Natl. Acad. Sci. USA 44, 223-228, 617-619 (1958); L. Brown and J. Schwinger, "Spin and Statistics," Prog. Theor. Phys. 26 (6), 917-926 (1961).
6. J. Schwinger, "Spin, Statistics and the TCP Theorem, and Addendum," Proc. Natl. Acad. Sci. USA 44, 223-228, 617-619 (1958); L. Brown and J. Schwinger, "Spin and Statistics," Prog. Theor. Phys. 26 (6), 917-926 (1961).
7. J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Redwood City, CA, 1988), Vol. I, pp. 134-144.
8. W. Pauli and V. F. Weisskopf, "On the Quantization of the Scalar Relativistic Wave Equation" Helv. Phys. Acta 7, 709-731 (1934).
9. W. Pauli, "Relativistic Quantized Theory of Particles Obeying Bose-Einstein Statistics," Ann. Inst. H. Poincaré 6, 137-152 (1936).
10. D. Iwanenko and A. Socolow, "Note on the Second Quantization of the Dirac Equation," Phys. Z. Sowjetunion 11, 590-596 (1937).
11. M. Fierz, "On the Relativistic Theory of Force Free Particles of Arbitrary Spin," Helv. Phys. Acta 12, 3-37 (1939).
12. F. J. Belinfante, "The Undor Equation of the Meson Field," Physica VI (9), 870-886 (1939).
13. W. Pauli and F. J. Belinfante, "On the Statistical Behavior of Known and Unknown Elementary Particles," Physica VII (3), 177-192 (1940).
14. J. S. de Wet, "On the Connection Between the Spin and Statistics of Elementary Particles," Phys. Rev. 57, 646-652 (1940); Ph.D. thesis, Princeton University, 1939.
15. W. Pauli, "On the Connection Between Spin and Statistics," Prog. Theor. Phys. 5 (4), 526-543 (1950).
16. R. P. Feynman, "The Theory of Positrons," Phys. Rev. 76, 749-759 (1949).
17. J. Schwinger, "The Theory of Quantized Fields. I," Phys. Rev. 82, 914-927 (1951).
18. G. Lüders and B. Zumino, "Connection Between Spin and Statistics," Phys. Rev. 110, 1450-1453 (1958).
19. N. Burgoyne, "On the Connection of Spin and Statistics," Nuovo Cimento VIII (4), 607-609 (1958).
20. A. S. Wightman, "Quantum Field Theory in Terms of Vacuum Expectation Values," Phys. Rev. 101, 860-866 (1956); D. Hall and A. S. Wightman, "A Theorem on Invariant Analytic Functions with Applications to Relativistic Quantum Field Theory," Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 31 (5), 1-41 (1957).
21. A. S. Wightman, "Quantum Field Theory in Terms of Vacuum Expectation Values," Phys. Rev. 101, 860-866 (1956); D. Hall and A. S. Wightman, "A Theorem on Invariant Analytic Functions with Applications to Relativistic Quantum Field Theory," Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 31 (5), 1-41 (1957).
22. R. Jost, "The Pauli Principle and the Lorentz Group," in Theoretical Physics in the Twentieth Century: A Memorial Volume to Wolfgang Pauli, edited by M. Fierz and V. F. Weisskopf (Interscience, New York, 1960), pp. 107-136.
23. E. C. G. Sudarshan, "The Fundamental Theorem on the Connection Between Spin and Statistics," in Proceedings of the Nobel Symposium 8, edited by N. Svartholm (Almquist and Wiksell, Stockholm, 1968), pp. 379-386. Many of these classic papers are contained in I. Duck and E. C. G. Sudarshan, Pauli and the Spin-Statistics Theoremm (World Scientific, Singapore, 1997).
24. E. C. G. Sudarshan, "The Fundamental Theorem on the Connection Between Spin and Statistics," in Proceedings of the Nobel Symposium 8, edited by N. Svartholm (Almquist and Wiksell, Stockholm, 1968), pp. 379-386. Many of these classic papers are contained in I. Duck and E. C. G. Sudarshan, Pauli and the Spin-Statistics Theoremm (World Scientific, Singapore, 1997).
25. P. A. M. Dirac, "The Quantum Theory of the Electron," Proc. R. Soc. London, Ser. A 117, 610-624 (1928).
26. P. A. M. Dirac, "A Theory of Electrons and Protons," Proc. R. Soc. London, Ser. A 126, 360-365 (1930); see The Principles of Quantum Mechanics (Oxford U.P., London, 1956), 3rd ed., pp. 272-274.
27. P. A. M. Dirac, "A Theory of Electrons and Protons," Proc. R. Soc. London, Ser. A 126, 360-365 (1930); see The Principles of Quantum Mechanics (Oxford U.P., London, 1956), 3rd ed., pp. 272-274.
28. P. Jordan, "On the Quantum Mechanics of the Degenerate Gas," Z. Phys. 44, 473-480 (1927); P. Jordan and E. Wigner, "On the Pauli Exclusion Principle," ibid. 47, 631-651 (1928).
29. P. Jordan, "On the Quantum Mechanics of the Degenerate Gas," Z. Phys. 44, 473-480 (1927); P. Jordan and E. Wigner, "On the Pauli Exclusion Principle," ibid. 47, 631-651 (1928).
30. F. Reines and H. W. Sobel, "Test of the Pauli Exclusion Principle for Atomic Electrons," Phys. Rev. Lett. 32, 954 (1974); E. Ramberg and G. Snow, "Experimental Limit on a Small Violation of the Pauli Principle," Phys. Lett. B 238, 438-441 (1995). In a different vein, K. Deilamian, J. D. Gillaspy, and D. E. Kelleher, "Search for Small Violations of the Symmetrization Postulate in an Excited State of Helium," Phys. Rev. Lett. 74, 4787-4790 (1995); M. de Angelis, G. Gagliardi, L. Gianfrani, and G. M. Tino, "Test of the Symmetrization Postulate for Spin-0 Particles," ibid. 76, 2840-2843 (1996); R. C. Hilborn and C. L. Yuca, "Spectroscopic Test of the Symmetrization Postulate for Spin-0 Nuclei," ibid. 76, 2844-2847 (1996).
31. F. Reines and H. W. Sobel, "Test of the Pauli Exclusion Principle for Atomic Electrons," Phys. Rev. Lett. 32, 954 (1974); E. Ramberg and G. Snow, "Experimental Limit on a Small Violation of the Pauli Principle," Phys. Lett. B 238, 438-441 (1995). In a different vein, K. Deilamian, J. D. Gillaspy, and D. E. Kelleher, "Search for Small Violations of the Symmetrization Postulate in an Excited State of Helium," Phys. Rev. Lett. 74, 4787-4790 (1995); M. de Angelis, G. Gagliardi, L. Gianfrani, and G. M. Tino, "Test of the Symmetrization Postulate for Spin-0 Particles," ibid. 76, 2840-2843 (1996); R. C. Hilborn and C. L. Yuca, "Spectroscopic Test of the Symmetrization Postulate for Spin-0 Nuclei," ibid. 76, 2844-2847 (1996).
32. F. Reines and H. W. Sobel, "Test of the Pauli Exclusion Principle for Atomic Electrons," Phys. Rev. Lett. 32, 954 (1974); E. Ramberg and G. Snow, "Experimental Limit on a Small Violation of the Pauli Principle," Phys. Lett. B 238, 438-441 (1995). In a different vein, K. Deilamian, J. D. Gillaspy, and D. E. Kelleher, "Search for Small Violations of the Symmetrization Postulate in an Excited State of Helium," Phys. Rev. Lett. 74, 4787-4790 (1995); M. de Angelis, G. Gagliardi, L. Gianfrani, and G. M. Tino, "Test of the Symmetrization Postulate for Spin-0 Particles," ibid. 76, 2840-2843 (1996); R. C. Hilborn and C. L. Yuca, "Spectroscopic Test of the Symmetrization Postulate for Spin-0 Nuclei," ibid. 76, 2844-2847 (1996).
33. F. Reines and H. W. Sobel, "Test of the Pauli Exclusion Principle for Atomic Electrons," Phys. Rev. Lett. 32, 954 (1974); E. Ramberg and G. Snow, "Experimental Limit on a Small Violation of the Pauli Principle," Phys. Lett. B 238, 438-441 (1995). In a different vein, K. Deilamian, J. D. Gillaspy, and D. E. Kelleher, "Search for Small Violations of the Symmetrization Postulate in an Excited State of Helium," Phys. Rev. Lett. 74, 4787-4790 (1995); M. de Angelis, G. Gagliardi, L. Gianfrani, and G. M. Tino, "Test of the Symmetrization Postulate for Spin-0 Particles," ibid. 76, 2840-2843 (1996); R. C. Hilborn and C. L. Yuca, "Spectroscopic Test of the Symmetrization Postulate for Spin-0 Nuclei," ibid. 76, 2844-2847 (1996).
34. F. Reines and H. W. Sobel, "Test of the Pauli Exclusion Principle for Atomic Electrons," Phys. Rev. Lett. 32, 954 (1974); E. Ramberg and G. Snow, "Experimental Limit on a Small Violation of the Pauli Principle," Phys. Lett. B 238, 438-441 (1995). In a different vein, K. Deilamian, J. D. Gillaspy, and D. E. Kelleher, "Search for Small Violations of the Symmetrization Postulate in an Excited State of Helium," Phys. Rev. Lett. 74, 4787-4790 (1995); M. de Angelis, G. Gagliardi, L. Gianfrani, and G. M. Tino, "Test of the Symmetrization Postulate for Spin-0 Particles," ibid. 76, 2840-2843 (1996); R. C. Hilborn and C. L. Yuca, "Spectroscopic Test of the Symmetrization Postulate for Spin-0 Nuclei," ibid. 76, 2844-2847 (1996).
35. R. D. Amado and H. Primakoff, "Comments on Testing the Pauli Principle," Phys. Rev. C 22, 1338-1340 (1980).
36. W. Heisenberg, "Many-Body Problem and Resonance in Quantum Mechanics," Z. Phys. 38, 411-426 (1926); P. A. M. Dirac, "On the Theory of Quantum Mechanics," Proc. R. Soc., London, Ser. A 112, 661-677 (1926).
37. W. Heisenberg, "Many-Body Problem and Resonance in Quantum Mechanics," Z. Phys. 38, 411-426 (1926); P. A. M. Dirac, "On the Theory of Quantum Mechanics," Proc. R. Soc., London, Ser. A 112, 661-677 (1926).
38. O. W. Greenberg and R. N. Mohapatra, "Phenomenology of Small Violations of Fermi and Bose Statistics," Phys. Rev. D 39, 2032-2038 (1989); "Local Quantum Field Theory of Possible Violations of the Pauli Principle," Phys. Rev. Lett. 59, 2507-2510 (1987); A. M. L. Messiah and O. W. Greenberg, "Symmetrization Postulate and Its Experimental Foundation," Phys. Rev. B 136, 248-267 (1964); A. Y. Ignatiev and V. A. Kuzmin, "Search for Slight Violations of the Pauli Principle," JETP Lett. 47, 4-7 (1988).
39. O. W. Greenberg and R. N. Mohapatra, "Phenomenology of Small Violations of Fermi and Bose Statistics," Phys. Rev. D 39, 2032-2038 (1989); "Local Quantum Field Theory of Possible Violations of the Pauli Principle," Phys. Rev. Lett. 59, 2507-2510 (1987); A. M. L. Messiah and O. W. Greenberg, "Symmetrization Postulate and Its Experimental Foundation," Phys. Rev. B 136, 248-267 (1964); A. Y. Ignatiev and V. A. Kuzmin, "Search for Slight Violations of the Pauli Principle," JETP Lett. 47, 4-7 (1988).
40. O. W. Greenberg and R. N. Mohapatra, "Phenomenology of Small Violations of Fermi and Bose Statistics," Phys. Rev. D 39, 2032-2038 (1989); "Local Quantum Field Theory of Possible Violations of the Pauli Principle," Phys. Rev. Lett. 59, 2507-2510 (1987); A. M. L. Messiah and O. W. Greenberg, "Symmetrization Postulate and Its Experimental Foundation," Phys. Rev. B 136, 248-267 (1964); A. Y. Ignatiev and V. A. Kuzmin, "Search for Slight Violations of the Pauli Principle," JETP Lett. 47, 4-7 (1988).
41. O. W. Greenberg and R. N. Mohapatra, "Phenomenology of Small Violations of Fermi and Bose Statistics," Phys. Rev. D 39, 2032-2038 (1989); "Local Quantum Field Theory of Possible Violations of the Pauli Principle," Phys. Rev. Lett. 59, 2507-2510 (1987); A. M. L. Messiah and O. W. Greenberg, "Symmetrization Postulate and Its Experimental Foundation," Phys. Rev. B 136, 248-267 (1964); A. Y. Ignatiev and V. A. Kuzmin, "Search for Slight Violations of the Pauli Principle," JETP Lett. 47, 4-7 (1988).
42. H. S. Green, "A Generalized Method of Field Quantization," Phys. Rev. 90, 270-273 (1953); J. L. Richard and E. C. G. Sudarshan, "Statistical Mechanics of Parafermi Systems," J. Math. Phys. 14, 1170-1175 (1973).
43. H. S. Green, "A Generalized Method of Field Quantization," Phys. Rev. 90, 270-273 (1953); J. L. Richard and E. C. G. Sudarshan, "Statistical Mechanics of Parafermi Systems," J. Math. Phys. 14, 1170-1175 (1973).
44. O. W. Greenberg, "Particles with Small Violations of Fermi or Bose Statistics," Phys. Rev. D 43, 4111-4120 (1991); "Interactions of Particles Having Small Violations of Statistics," Physica A 180, 419-427 (1992).
45. O. W. Greenberg, "Particles with Small Violations of Fermi or Bose Statistics," Phys. Rev. D 43, 4111-4120 (1991); "Interactions of Particles Having Small Violations of Statistics," Physica A 180, 419-427 (1992).
46. O. W. Greenberg, D. M. Greenberger, and T. V. Greenbergest, "(Para) Bosons, (Para) Fermions, Quons and other Beasts in the Menagerie of Particle Statistics," in Quantum Coherence and Reality, edited by J. S. Anandan and J. L. Safko (World Scientific, Singapore, 1994), pp. 306-318.
47. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1965), Vol. 3, Chap. 4.
48. H. Bacry, "Answer to Question #7 ['The spin-statistics theorem,' D. E. Neuenschwander]," Am, J. Phys. 63 (4), 297-298 (1995).
49. A. A. Bṙoyles, "Spin and Statistics," Am. J. Phys. 44 (4), 340 (1976).
50. R. R. Gould, "Answer to Question #7 ['The spin-statistics theorem,' D. E. Neuenschwander]," Am. J. Phys. 63 (2), 109 (1995).
51. R. P. Feynman, "The Reasons for Antiparticles," in Elementary Particles and the Laws of Physics. The 1986 Dirac Memorial Lectures, edited by R. P. Feynman and S. Weinberg (Cambridge U.P., New York, 1987), pp. 56-59.
52. T. von Foerster, "Answer to Question #7 ['The spin-statistics theorem,' D. E. Neuenschwander]," Am. J. Phys. 64 (5), 526 (1996).
53. M. Saha, "On the Origin of Mass in Neutrons and Protons," Indian J. Phys. 10, 145-147 (1936) "Note on Dirac's Theory of Magnetic Poles," Phys. Rev. 75, 1968 (1949); H. A. Wilson, "Note on Dirac's Theory of Magnetic Poles," ibid. 75, 908 (1949); J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed., pp. 251-260.
54. M. Saha, "On the Origin of Mass in Neutrons and Protons," Indian J. Phys. 10, 145-147 (1936) "Note on Dirac's Theory of Magnetic Poles," Phys. Rev. 75, 1968 (1949); H. A. Wilson, "Note on Dirac's Theory of Magnetic Poles," ibid. 75, 908 (1949); J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed., pp. 251-260.
55. M. Saha, "On the Origin of Mass in Neutrons and Protons," Indian J. Phys. 10, 145-147 (1936) "Note on Dirac's Theory of Magnetic Poles," Phys. Rev. 75, 1968 (1949); H. A. Wilson, "Note on Dirac's Theory of Magnetic Poles," ibid. 75, 908 (1949); J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed., pp. 251-260.
56. M. Saha, "On the Origin of Mass in Neutrons and Protons," Indian J. Phys. 10, 145-147 (1936) "Note on Dirac's Theory of Magnetic Poles," Phys. Rev. 75, 1968 (1949); H. A. Wilson, "Note on Dirac's Theory of Magnetic Poles," ibid. 75, 908 (1949); J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed., pp. 251-260.
57. D. Finkelstein, "Internal Structure of Spinning Particles," Phys. Rev. 100, 924 (1955); D. Finkelstein and J. Rubinstein, "Connection Between Spin, Statistics, and Kinks," J. Math. Phys. 9 (11), 1762-1778 (1968); L. Schulman, "A Path Integral for Spin," Phys. Rev. 176, 1558-1569 (1968).
58. D. Finkelstein, "Internal Structure of Spinning Particles," Phys. Rev. 100, 924 (1955); D. Finkelstein and J. Rubinstein, "Connection Between Spin, Statistics, and Kinks," J. Math. Phys. 9 (11), 1762-1778 (1968); L. Schulman, "A Path Integral for Spin," Phys. Rev. 176, 1558-1569 (1968).
59. D. Finkelstein, "Internal Structure of Spinning Particles," Phys. Rev. 100, 924 (1955); D. Finkelstein and J. Rubinstein, "Connection Between Spin, Statistics, and Kinks," J. Math. Phys. 9 (11), 1762-1778 (1968); L. Schulman, "A Path Integral for Spin," Phys. Rev. 176, 1558-1569 (1968).
60. L. C. Biedenharn and J. D. Louck, "Angular Momentum in Quantum Mechanics. Theory and Application," in Encyclopedia of Mathematics and its Applications, edited by G.-C. Rota and P. A. Carruthers (Addison-Wesley, Reading, MA, 1981), Chap. 2, pp. 7-26.
61. T. D. Imbo, C. S. Imbo, and E. C. G. Sudarshan, "Identical Particles, Exotic Statistics and Braid Groups," Phys. Lett. B 234, 103-107 (1990).
62. A. P. Balachandran, A. Daughton, Z.-C. Gu, R. D. Sorkin, G. Marmo, and A. M. Srivastava, "Spin-Statistics Theorems Without Relativity or Field Theory." Int. J. Mod. Phys. A 8, 2993-3044 (1993).
63. M. V. Berry and J. M. Robbins, "Indistinguishability for quantum particles: Spin, statistics and the geometric phase," Proc. R. Soc. London Ser. A 453, 1771-1790 (1997).
64. R. P. Feynman, "Space-Time Approach to Quantum Electrodynamics," Phys. Rev. 76, 769-789 (1949); J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964), pp. 95, 188.
65. R. P. Feynman, "Space-Time Approach to Quantum Electrodynamics," Phys. Rev. 76, 769-789 (1949); J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964), pp. 95, 188.
66. J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965), pp. 139, 227; S. Weinberg, The Quantum Theory of Fields (Cambridge U.P., New York, 1995), pp. 447-462.
67. J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965), pp. 139, 227; S. Weinberg, The Quantum Theory of Fields (Cambridge U.P., New York, 1995), pp. 447-462.
68. E. C. G. Sudarshan, "Relation Between Spin and Statistics," Stat. Phys. Suppl.: J. Indian Inst. Sci. June, 123-137 (1975).
69. W. Pauli, "On Dirac's New Method of Field Quantization," Rev. Mod. Phys. 15, 175-207 (1943).
70. S. Weinberg, in Ref. 45, p. 204.
71. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, 1957), pp. 80, 46; A. March, Quantum Mechanics of Particles and Wave Fields (Wiley, New York, 1951), pp. 140, 150.
72. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, 1957), pp. 80, 46; A. March, Quantum Mechanics of Particles and Wave Fields (Wiley, New York, 1951), pp. 140, 150.
73. H. Fort and R. Gambini, "Fractional Statistics in Three Dimensions: Compact Maxwell-Higgs System," Phys. Rev. D 54, 1778-1781 (1996).
74. K. Johnson and E. C. G. Sudarshan, "Inconsistency of the Local Field Theory of Charged Spin-3/2 Particles," Ann. Phys. 13, 126-145 (1961).
75. The higher spin particles of supersymmetry require path integral quantization and a "ghost" mechanism to eliminate wrong-sign anticommutators. They are not included in Johnson and Sudarshan's proof which is based on canonical field theory.
76. F. A. Berezin, Introduction to Superanalysis, edited by A. A. Kirillov (Reidel, Boston, 1988), App. 1, pp. 374-403; M. Kaku, Quantum Field Theory, A Modern Introduction (Oxford U.P., New York, 1993), pp. 285- 289; J. L. Martin, "The Feynman Principle for a Fermi System," Proc. R. Soc. London, Ser. A 251, 543 (1959).
77. F. A. Berezin, Introduction to Superanalysis, edited by A. A. Kirillov (Reidel, Boston, 1988), App. 1, pp. 374-403; M. Kaku, Quantum Field Theory, A Modern Introduction (Oxford U.P., New York, 1993), pp. 285-289; J. L. Martin, "The Feynman Principle for a Fermi System," Proc. R. Soc. London, Ser. A 251, 543 (1959).
78. F. A. Berezin, Introduction to Superanalysis, edited by A. A. Kirillov (Reidel, Boston, 1988), App. 1, pp. 374-403; M. Kaku, Quantum Field Theory, A Modern Introduction (Oxford U.P., New York, 1993), pp. 285- 289; J. L. Martin, "The Feynman Principle for a Fermi System," Proc. R. Soc. London, Ser. A 251, 543 (1959).
79. P. Roman, Theory of Elementary Particles (North-Holland, Amsterdam, 1960), pp. 125-126.