Quantization of Fractional Singular Lagrangian systems with Second-Order Derivatives Using Path Integral Method

TL;DR

This paper develops a fractional path integral quantization method for singular Lagrangian systems with second-order derivatives, extending classical quantization techniques into fractional calculus.

Contribution

It introduces a novel fractional path integral framework for quantizing singular systems with higher derivatives, including the formulation of fractional Hamilton-Jacobi equations.

Findings

Fractional equations of motion are derived for singular systems.

A fractional path integral quantization scheme is constructed.

The method is applied to a system with two primary first class constraints.

Abstract

The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also, the set of Hamilton Jacobi partial differential equations is constructed in fractional form. The path integral formulation and path integral quantization for these systems are constructed within fractional derivatives. We examined a mathematical singular Lagrangian with two primary first class constraints.