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An extended phase-space stochastic quantization of constrained Hamiltonian systems. (English) Zbl 1195.81084
Summary: Having gained some insight into the concept of actual and virtual paths’ in a phase-space formalism [{\it Y. Sobouti} and {\it S. Nasiri}, Int. J. Mod. Phys. B 7, 3255 (1993); {\it S. Nasiri, Y. Sobouti} and {\it F. Taati}, J. Math. Phys. 47, No. 9, 092106 15 p. (2006; Zbl 1112.81069)], in the present paper we address the question of extended’ phase-space stochastic quantization of Hamiltonian systems with first class holonomic constraints. We present the appropriate Langevin equations, which quantize such constrained systems, and prove the equivalence of the stochastic quantization method with the conventional path-integral gauge measure of Faddeev-Popov quantization.

##### MSC:
 81S30 Phase space methods in quantum mechanics 81S20 Stochastic quantization
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