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Projection operator approach to the quantization of higher spin fields

  • Gábor Zsolt TóthEmail author
Regular Article - Theoretical Physics

Abstract

A general method to construct free quantum fields for massive particles of arbitrary definite spin in a canonical Hamiltonian framework is presented. The main idea of the method is as follows: a multicomponent Klein–Gordon field that satisfies canonical (anti)commutation relations and serves as an auxiliary higher spin field is introduced, and the physical higher spin field is obtained by acting on the auxiliary field by a suitable differential operator. This allows the calculation of the (anti)commutation relations, the Green functions and the Feynman propagators of the higher spin fields. In addition, canonical equations of motions, which are expressed in terms of the auxiliary variables, can be obtained also in the presence of interactions, if the interaction Hamiltonian operator is known. The fields considered transform according to the (n/2,m/2)⊕(m/2,n/2) and (n/2,m/2) representations of the Lorentz group.

Keywords

Gordon Equation Hamiltonian Operator Mode Expansion Anticommutation Relation Dirac Field 
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References

  1. 1.
    P.A.M. Dirac, Proc. R. Soc. A 155, 447 (1936) ADSCrossRefGoogle Scholar
  2. 2.
    M. Fierz, Helv. Phys. Acta 12, 3 (1939) CrossRefGoogle Scholar
  3. 3.
    M. Fierz, W. Pauli, Proc. R. Soc. A 173, 211 (1939) MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    W. Rarita, J. Schwinger, Phys. Rev. 60, 61 (1941) ADSzbMATHCrossRefGoogle Scholar
  5. 5.
    V. Bargmann, E.P. Wigner, Proc. Natl. Acad. Sci. USA 34, 211 (1948) MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. 6.
    S. Weinberg, Phys. Rev. 133, B1318 (1964) MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    S. Weinberg, Phys. Rev. 134, B882 (1964) MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    S. Weinberg, The quantum theory of fields, vol. I (Cambridge University Press, Cambridge, 1995–2000) Google Scholar
  9. 9.
    D.N. Williams, Lectures in Theoretical Physics, vol. VIIa (University of Colorado Press, Boulder, 1965), p. 139 Google Scholar
  10. 10.
    C. Lorcé, Phys. Rev. D 79, 113011 (2009) ADSCrossRefGoogle Scholar
  11. 11.
    N.A. Doughty, R.A. Arnold, J. Math. Phys. 30 (1989) Google Scholar
  12. 12.
    J.W. Wagenaar, T.A. Rijken, Phys. Rev. D 80, 104027 (2009) ADSCrossRefGoogle Scholar
  13. 13.
    H. Shi-Zhong, R. Tu-Nan, W. Ning, Z. Zhi-Peng, Eur. Phys. J. C 26, 609–623 (2003) ADSzbMATHCrossRefGoogle Scholar
  14. 14.
    H. Shi-Zhong, Z. Peng-Fei, R. Tu-Nan, Z. Yu-Can, Z. Zhi-Peng, Eur. Phys. J. C 42, 375–389 (2005) ADSCrossRefGoogle Scholar
  15. 15.
    H. Umezawa, A. Visconti, Nucl. Phys. 1, 348 (1956) MathSciNetzbMATHGoogle Scholar
  16. 16.
    A. Aurilia, H. Umezawa, Phys. Rev. 182, 1682 (1969) MathSciNetADSzbMATHCrossRefGoogle Scholar
  17. 17.
    C. Fronsdal, Nuovo Cimento 9(Suppl. 2), 416 (1958) MathSciNetGoogle Scholar
  18. 18.
    G. Velo, D. Zwanziger, Phys. Rev. 186, 1337–1341 (1969) ADSCrossRefGoogle Scholar
  19. 19.
    J. Madore, Phys. Lett. B 55, 217–218 (1975) ADSCrossRefGoogle Scholar
  20. 20.
    S. Deser, A. Waldron, V. Pascalutsa, Phys. Rev. D 62, 105031 (2000) MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    A. Shamaly, A.Z. Capri, Ann. Phys. 74, 503 (1972) ADSCrossRefGoogle Scholar
  22. 22.
    J. Frauendiener, J. Phys. A, Math. Gen. 36, 8433–8442 (2003) MathSciNetADSzbMATHCrossRefGoogle Scholar
  23. 23.
    B. Schroer, R. Seiler, J.A. Swieca, Phys. Rev. D 2, 2927 (1970) MathSciNetADSzbMATHCrossRefGoogle Scholar
  24. 24.
    D.V. Ahluwalia, D.J. Ernst, Phys. Rev. C 45, 3010 (1992) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Institute for Particle and Nuclear Physics, Wigner Research Centre for PhysicsHungarian Academy of SciencesBudapestHungary

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