Summary: Having gained some insight into the concept of ‘actual and virtual paths’ in a phase-space formalism [Y. Sobouti
and S. Nasiri
, Int. J. Mod. Phys. B 7, 3255 (1993); S. Nasiri, Y. Sobouti
and 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.