Canonical path integral quantization of the finite dimensional systems with constraints

TL;DR

This paper presents a canonical path integral quantization method for finite-dimensional constrained systems that simplifies the treatment of constraints without gauge fixing or enlarging phase space.

Contribution

It introduces a unified approach to path integral quantization for constrained systems that avoids distinguishing constraint classes and gauge fixing.

Findings

Successfully applied to three singular systems

No need to differentiate between first and second-class constraints

Eliminates the requirement for gauge fixing and phase space enlargement

Abstract

The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space coordinates. The path integral is obtained as an integration over the canonical phase space coordinates. This approach is applied to obtain the path integral for three singular systems and it is shown that in our formulation there is no need to distinguish between first and second-class constraints, no need for fixing any gauge, as will as no need to enlarge the phase space.