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