Abstract
The properties of second-class constraints and their Dirac brackets are reviewed using a finite-dimensional mechanical model. Following the general formulation, the simplification which results when the constraints can be solved for canonical pairs of variables is obtained. Finally, the case where all the constrained momenta vanish is treated. This case corresponds to the second-class constraints which arise in the canonical formulation of a field theory on a null surface. In this case we show that not only are the constrained variables given by the explicit solution, but the Dirac brackets of the unconstrained variables are equal to their original Poisson brackets.
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References
P. A. M. DiracProc. Roy. Soc. London A246 333 (1958).
P. A. M. Dirac Phys. Rev . 114 924 (1959).
P. G. Bergmann and A. Komar, Phys. Rev. Lett. 4 432 (1960).
K. Sundenneyer, Constrained Dynamics, Springer-Verlag, Berlin (1982).
E. C. G. Sudarshan and N. Mukunda, Classical Mechanics: A Modern Perspective, John Wiley and Sons, New York (1974).
M. Henneaux and C. Teitelboim, Quantization ofGauge Systems, Princeton University Press, Princeton, NJ (1992).
J. N. GoldbergFound. Phys. 15 439 (1985).
C. TorreClass. Quant. Gray. 3, 773 (1986).
J. N. Goldberg, D.C. Robinson, and C Soteriou, Class. Quant. Gray. 9 1309 (1992).
R. d’Inverno and J. Vickers, Class. Quant. Gray. 12 753 (1995).
J. N. Goldberg and C Soteriou, Class. Quant. Gray. 12 2779 (1995).
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Goldberg, J.N. (1999). Second-Class Constraints. In: Harvey, A. (eds) On Einstein’s Path. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1422-9_17
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DOI: https://doi.org/10.1007/978-1-4612-1422-9_17
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7137-6
Online ISBN: 978-1-4612-1422-9
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