Gauge-variance of the Dirac bracket
- 35 Downloads
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
Unable to display preview. Download preview PDF.
- Dirac, P. A. M. (1950).Canadian Journal of Mathematics,2,129.Google Scholar
- Dirac, P. A. M. (1951).Canadian Journal of Mathematics,3, 1.Google Scholar
- Dirac, P. A. M. (1958).Proceedings of the Royal Society (London), Series A,246, 326.Google Scholar
- Dirac, P. A. M. (1964).Lectures on Quantum Mechanics, Belfer Graduate School of Sciences Monograph Series No. 2. Yeshiva University, New York.Google Scholar
- Franke, W. H. and Kálnay, A. J. (1970).Journal of Mathematical Physics,11, 1729.Google Scholar
- Kálnay, A. J. and Ruggeri, G. J. (1972).International Journal of Theoretical Physics, Vol. 6, No. 3, p. 167.Google Scholar
- Kálnay, A. J. (1973).International Journal of Theoretical Physics, Vol. 7, No. 2, p. 119.Google Scholar
- Levy-Leblond, J. M. (1969).Communications in Mathematical Physics,12, 64.Google Scholar