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Il Nuovo Cimento (1955-1965)

, Volume 20, Issue 4, pp 773–790 | Cite as

Solution of the equations for the green’s functions of a two dimensional relativistic field theory

  • K. Johnson
Article

Summary

The explicit solution of the coupled set of equations for the Green’s functions for the self-coupled field theory model of Thirring is given. It is found that the infra-red problem causes no special difficulty. The question of how to define products of singular field operators at coincident space-time points arises and it is shown that the commutation relations for such products are not consistently given by making use of the formal expressions and the canonical commutation relations. The problem of gauge invariance in an external field is studied and it is shown that:a) the current and charge density do not commute at equal times, andb) this is necessary for and consistent with the gauge invariance of the field equations.

Riassunto

Si dà la soluzione esplicita del gruppo accoppiato di equazioni per le funzioni di Green per il modello auto-accoppiato della teoria del campo di Thirring. Si trova che il problema infrarosso non genera particolare difficoltà. Sorge la questione sul modo di definire i prodotti degli operatori di campo singolari in punti coincidenti dello spaziotempo e si mostra che le relazioni di commutazione per questi prodotti non vengono espresse coerentemente facendo uso delle espressioni formali e delle relazioni di commutazione canonica. Si studia il problema della invarianza di gauge in un campo esterno e si mostraa) che la corrente e la densità di carica non commutano in tempi uguali, eb) che questo è necessario per l’invarianza di gauge delle equazioni del campo, e coerente con essa.

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References

  1. (1).
    W. Thirring:Ann. of Phys.,3, 91 (1958).MathSciNetADSCrossRefGoogle Scholar
  2. (2).
    V. Glaser:Nuovo Cimento,9, 990 (1958).F. Scarf:Phys. Rev.,117, 868 (1960).T. Pradhan:Nucl. Phys.,9, 124 (1958–59).MathSciNetCrossRefGoogle Scholar
  3. (3).
    Y. Takahashi:Nuovo Cimento,6, 371 (1957).CrossRefGoogle Scholar
  4. (6).
    P. Federbush andK. Johnson:Phys. Rev.,120, 1926 (1960).MathSciNetADSCrossRefGoogle Scholar
  5. (7).
    K. Johnson andB. Zumino:Phys. Rev. Lett.,3, 351 (1959).ADSCrossRefGoogle Scholar
  6. (8).
    J. Schwinger:Phys. Rev.,82, 664 (1951).MathSciNetADSCrossRefGoogle Scholar
  7. (9).
    F. L. Scarf:Nucl. Phys.,11, 475 (1959).CrossRefGoogle Scholar
  8. (10).
    K. Johnson: to be published.Google Scholar
  9. (11).
    J. Schwinger:Phys. Rev. Lett.,3, 296 (1959).ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1961

Authors and Affiliations

  • K. Johnson
    • 1
  1. 1.Department of Physics and Laboratory of Nuclear ScienceMassachusetts Institute of TechnologyCambridge

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