Path Integral Quantization of Constrained Systems

Abstract

In this thesis some singular physical systems are quantized using the canonical formulation and the Dirac’s method. The two methods represent the Hamiltonian treatment of the constrained systems. Dirac’s method introduced the primary constraints, then constructing the total Hamiltonian. The consistency conditions are checked on the primary constraints. The equations of motion in this method are in ordinary differential equation form. In the canonical method the equations of motion are total differential equations in many variables. These equations are integrable if the integrability conditions are identically satisfied. Path integral quantization of three different systems, are studied, free relativistic spinless particle, relativistic spinless particle in an external electromagnetic field and a charged particle moving in a constant magnetic field. In the study, the integrability conditions are satisfied, so the systems are integrable. Consequently the path integral quantization is obtained directly as an integration over the canonical reduced phase space coordinates. This makes the canonical method simpler than Dirac’s method.