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On the quantization of constrained systems using path integral techniques

Eqab M. Rabei

Published Oct 1, 2000• 5 citations
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Having gained some insight into the concept of 'actual and virtual paths' in a phase-space formalism (Sobouti and Nasiri 1993 Int. J. Mod. Phys. B 7 3255, Nasiri et al 2006 J. Math. Phys. 47 092106), 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.

Journal of Physics A Mathematical and Theoretical•Jul 4, 2008•4 citations
The concept of constrained Hamiltonian dynamical systems and their quantization, introduced by Dirac, constitutes one of the most fundamental contributions to the development of the canonical formalism in recent times. Dirac’s concepts were later incorporated into the path-integral formulation of quantum mechanics by Faddeev, which played an important role in understanding some subtle aspects in the quantization of non-Abelian gauge theory. An example is given from nonrelativistic quantum mechanics which illustrates the formalism through simple analogy.
Having gained some insight into the concept of 'actual and virtual paths' in a phase-space formalism (Sobouti and Nasiri 1993 Int. J. Mod. Phys. B 7 3255, Nasiri et al 2006 J. Math. Phys. 47 092106), 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.