Foundations of Physics

, Volume 45, Issue 7, pp 858–873 | Cite as

Proof of the Spin–Statistics Theorem

  • Enrico Santamato
  • Francesco De Martini


The traditional standard quantum mechanics theory is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle”. A complete and straightforward solution of the spin–statistics problem is presented on the basis of the “conformal quantum geometrodynamics” theory. This theory provides a Weyl-gauge invariant formulation of the standard quantum mechanics and reproduces successfully all relevant quantum processes including the formulation of Dirac’s or Schrödinger’s equation, of Heisenberg’s uncertainty relations and of the nonlocal EPR correlations. When the conformal quantum geometrodynamics is applied to a system made of many identical particles with spin, an additional constant property of all elementary particles enters naturally into play: the “intrinsic helicity”. This property, not considered in the Standard Quantum Mechanics, determines the correct spin–statistics connection observed in Nature.


Spin–statistics connection Intrinsic helicity Conformal quantum geometrodynamics 


  1. 1.
    Atre, M.V., Mukunda, N.: Classical particles with internal structure: general formalism and application to first-order internal spaces. J. Math. Phys. 27, 2908–2919 (1986)zbMATHMathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Balachandran, A.P., Daughton, A., Gu, Z.C., Sorkin, R.D., Marmo, G., Srivastava, A.M.: Spin-statistics theorems without relativity or field theory. Int. J. Mod. Phys. A 8(17), 2993–3044 (1993). doi: 10.1142/S0217751X93001223.
  3. 3.
    Biedenharn, L.C., Dam, H.V., Marmo, G., Morandi, G., Mukunda, N., Samuel, J., Sudarshan, E.C.G.: Classical models for Regge trajectories. Int. J. Mod. Phys. A 2, 1567–1589 (1987)ADSCrossRefGoogle Scholar
  4. 4.
    Bohm, D.: A suggested interpretation of the quantum theory in terms of “Hidden” variables I. Phys. Rev. 85(2), 166–179 (1952). doi: 10.1103/PhysRev.85.166
  5. 5.
    Bohm, D.: A suggested interpretation of the quantum theory in terms of “Hidden” variables II. Phys. Rev. 85(2), 180–193 (1952). doi: 10.1103/PhysRev.85.180
  6. 6.
    Bohm, D., Hiley, B.J.: The Undivided Universe: An Ontological Interpretation of Quantum Theory. Routledge, London (1995)zbMATHGoogle Scholar
  7. 7.
    Chew, G.F., Frautschi, S.C.: Regge trajectories and the principle of maximum strength for strong interactions. Phys. Rev. Lett. 8, 41–44 (1962)ADSCrossRefGoogle Scholar
  8. 8.
    Davydov, A.S.: Quantum Mechanics, 2, edition edn. Pergamon Pr, Oxford (1976)Google Scholar
  9. 9.
    De Broglie, L., Andrade e Silva, J.L.: La réinterprétation de la mécanique ondulatoire. Gauthier-Villars, Paris (1971)Google Scholar
  10. 10.
    De Martini, F., Santamato, E.: Derivation of Dirac’s equation from conformal differential geometry. In: D’Ariano, M., Fei, S.M., Haven, E., Hiesmayr, B., Jaeger, G., Khrennikov, A., Larsson, J.Å. (eds.) Foundations of Probability and Physics 6, vol. 1424, pp. 45–54. AIP Conference Proceedings 2012, (2011). doi: 10.1063/1.3688951
  11. 11.
    De Martini, F., Santamato, E.: Interpretation of quantum nonlocality by conformal quantum geometrodynamics. Int. J. Theor. Phys. 53(10), 3308–3322 (2014). doi: 10.1007/s10773-013-1651-y.
  12. 12.
    De Martini, F., Santamato, E.: Nonlocality, no-signalling, and Bell’s theorem investigated by Weyl conformal differential geometry. Phys. Scr. T163, 014015 (2014). doi: 10.1088/0031-8949/2014/T163/014015 ADSCrossRefGoogle Scholar
  13. 13.
    Dirac, P.A.M.: Long range forces and broken symmetries. Proc. R. Soc. Lond. Ser. A 333, 403–418 (1973)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Duck, I., Sudarshan, E.C.G.: Toward an understanding of the spin-statistics theorem. Am. J. Phys. 66(4), 284–303 (1998). doi: 10.1119/1.18860 zbMATHMathSciNetADSCrossRefGoogle Scholar
  15. 15.
    Duck, I., Sudarshan, E.C.G., Wightman, A.S.: Pauli and the spin-statistics theorem. Am. J. Phys. 67(8), 742–746 (1999). doi: 10.1119/1.19365 ADSCrossRefGoogle Scholar
  16. 16.
    Feynman, R.P., Leighton, R.B., Sands, M.L.: The Feynman Lectures on Physics, vol. III. Addison-Wesley, Redwood City (1989)Google Scholar
  17. 17.
    Goldstein, H.: Classical Mechanics. Addison-Wesley Pub. Co., Reading (1980)zbMATHGoogle Scholar
  18. 18.
    Hehl, F., Lemk, J., Mielke, E.: Two lectures on fermions and gravity. In: Debrus, J., Hirshfeld, A. (eds.) Geometry and Theoretical Physics, Bad Honnef Lectures, 12–16 Feb, pp. 56–140. Springer, Berlin (1991)CrossRefGoogle Scholar
  19. 19.
    Hochberg, D., Plunien, G.: Theory of matter in Weyl spacetime. Phys. Rev. D 43, 3358–3367 (1991). doi: 10.1103/PhysRevD.43.3358
  20. 20.
    Jabs, A.: Addendum to: connecting spin and statistics in quantum mechanics. Found. Phys. 40(7), 793–794 (2010). doi: 10.1007/s10701-009-9351-4 zbMATHMathSciNetADSCrossRefGoogle Scholar
  21. 21.
    Jabs, A.: Connecting spin and statistics in quantum mechanics. Found. Phys. 40(7), 776–792 (2010)zbMATHMathSciNetADSCrossRefGoogle Scholar
  22. 22.
    Khrennikov, A.: Towards a field model of prequantum reality. Found. Phys. 42(6), 725–741 (2011). doi: 10.1007/s10701-011-9611-y.
  23. 23.
    Khrennikov, A., Ohya, M., Watanabe, N.: Quantum probability from classical signal theory. Int. J. Quantum Inf. 09(supp01), 281–292 (2011). doi: 10.1142/S0219749911007289.
  24. 24.
    Lord, E.A.: Tensors, Relativity and Cosmology. McGraw-Hill, New York (1979)Google Scholar
  25. 25.
    Quigg, C.: Gauge Theories of the Strong. Weak and Electromagnetic Interactions. Benjamin, Menlo Park (1983)Google Scholar
  26. 26.
    Romer, R.H.: The spin-statistics theorem. Am. J. Phys. 70(8), 791–791 (2002). doi: 10.1119/1.1482064 ADSCrossRefGoogle Scholar
  27. 27.
    Salam, A., Strathdee, J.: On Kaluza-Klein theory. Ann. Phys. 141(2), 316–352 (1982). doi: 10.1016/0003-4916(82)90291-3 MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    Santamato, E.: Geometric derivation of the Schrödinger equation from classical mechanics in curved Weyl spaces. Phys. Rev. D 29(2), 216–222 (1984). doi: 10.1103/PhysRevD.29.216
  29. 29.
    Santamato, E.: Statistical interpretation of the Kleinâ Gordon equation in terms of the spaceâ time Weyl curvature. J. Math. Phys. 25(8), 2477–2480 (1984). doi: 10.1063/1.526467.
  30. 30.
    Santamato, E.: Gauge-invariant statistical mechanics and average action principle for the Klein-Gordon particle in geometric quantum mechanics. Phys. Rev. D 32(10), 2615–2621 (1985). doi: 10.1103/PhysRevD.32.2615
  31. 31.
    Santamato, E.: Heisenberg uncertainty relations and average space curvature in geometric quantum mechanics. Phys. Lett. A 130(4–5), 199–202 (1988). doi: 10.1016/0375-9601(88)90593-2.
  32. 32.
    Santamato, E., De Martini, F.: Solving the nonlocality riddle by conformal quantum geometrodynamics. Int. J. Quantum Inf. 10(08), 1241013 (2012). doi: 10.1142/S0219749912410134.
  33. 33.
    Santamato, E., De Martini, F.: Derivation of the Dirac equation by conformal differential geometry. Found. Phys. 43, 631–641 (2013). doi: 10.1007/s10701-013-9703-y zbMATHMathSciNetADSCrossRefGoogle Scholar
  34. 34.
    Taylor, J.R.: Classical Mechanics. University Science Books, Sausalito (2005)zbMATHGoogle Scholar
  35. 35.
    Weyl, H.: Gravitation und elektrizität. Sitzungsber. Preuss. Akad. Wiss. Phys. Math. K1, 465–480 (1918). Reprinted. In: The Principles of Relativity (Dover, New York, 1923)Google Scholar
  36. 36.
    Weyl, H.: Space, Time, Matter, 4th edn. Dover Publications Inc, New York (1952)Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Dipartimento di Scienze FisicheUniversità di Napoli Federico II, Complesso Universitario di Monte S. AngeloNapoliItaly
  2. 2.CNISM - Consorzio Nazionale Interuniversitario per la Struttura della MateriaNapoliItaly
  3. 3.Accademia Nazionale dei LinceiRomaItaly

Personalised recommendations