Symmetry in Nonlinear Mathematical Physics - 2009

Mikhail Krivoruchenko (Institute for Theoretical and Experimental Physics, Moscow, Russia & Institut für Theoretische Physik der Universität Tübingen, Germany)

Quantum deformation of the Dirac bracket

The quantum deformation of the Poisson bracket is the Moyal bracket. We construct quantum deformation of the Dirac bracket for systems which admit global symplectic basis for constraint functions. Equivalently, it can be considered as an extension of the Moyal bracket to second-class constraints systems and to gauge-invariant systems which become second class when gauge-fixing conditions are imposed.

[1] M.I. Krivoruchenko, A.A. Raduta, Amand Faessler, Phys.Rev. D73 (2006) 025008.