Gauge-variance of the Dirac bracket
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.
KeywordsField Theory Elementary Particle Quantum Field Theory Functional Form Classical Model
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