Path Integral Quantization of Regular Lagrangian

Ola A Jarab’ah

doi:10.5539/apr.v10n1p9

Abstract

Path integral formulation based on the canonical method is discussed. The Hamilton Jacobi function for regular Lagrangian is obtained using separation of variables method. This function is used to quantize regular systems using path integral method. The path integral is obtained as integration over the canonical phase space coordinates. One illustrative example is considered to demonstrate the application of our formalism.

Highlights

The path integral is an expression for the propagator in terms of an integral over an infinite dimensional space of paths in configuration space
Many important applications of path integral have been found in statistical physics, in the theory of phase transitions, super fluidity, super conductivity, quantum optics, and plasma physics
The path integral concept was introduced for the first time by (Wiener, 1921) as a method to solve problems in the theory of diffusion and Brownian motion. This integral which is called the Wiener integral has played a central role in the further development of the subject of path integration. It was reinvented in a different form by (Feynman, 1948), for the reformulation of quantum mechanics

Summary

Introduction

The path integral is an expression for the propagator in terms of an integral over an infinite dimensional space of paths in configuration space. The path integral concept was introduced for the first time by (Wiener, 1921) as a method to solve problems in the theory of diffusion and Brownian motion. This integral which is called the Wiener integral has played a central role in the further development of the subject of path integration. The purpose of the present work is to construct the Hamilton Jacobi function for regular Lagrangian using separation of variables technique in order to quantize the regular systems using path integral method.

Hamilton Jacobi Formulation and Path Integral Quantization

Illustrative Example

Conclusion