Gauge-variance of the Dirac bracket

  • A. J. Kálnay
  • G. J. Ruggeri


This work is devoted to the study of the change in the functional form of the minus Dirac bracket under pure gauge transformations (in the sense of Levy-Leblond). We found a closed formula which expresses this change and we use it to discuss the relevance of a gauge transformation for the skew-symmetric (Bose-like) quantization procedure of constrained classical models. We found necessary conditions which are to be fulfilled if the gauge transformation is to induce a mere change of representation at the quantum level. It is shown, by considering a simple example, that these conditions can be violated. We conclude then that adding a total time derivative to the Lagrangian of a classical model can drastically change the physical properties of the quantized Bose-like counterpart. A similar result has been detected previously for two particular systems quantized through the symmetric (Fermi-like) rule of quantization.


Field Theory Elementary Particle Quantum Field Theory Functional Form Classical Model 
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Copyright information

© Plenum Publishing Company Limited 1973

Authors and Affiliations

  • A. J. Kálnay
    • 1
  • G. J. Ruggeri
    • 2
  1. 1.Centro de FisicaInstituto Venezolano de Investigaciones CientlficasCaracasVenezuela
  2. 2.Departamento de Fisica, Facultad de CienciasUniversidad Central de VenezuelaCaracasVenezuela

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