Fractional Dirac Bracket and Quantization for Constrained Systems

TL;DR

This paper introduces a fractional calculus-based extension of Dirac brackets to systematically quantize dissipative and nonconservative systems, facilitating deeper analysis of gauge theories with second-class constraints.

Contribution

It proposes a novel fractional Dirac bracket formalism to handle dissipative systems and nonconservative theories within the canonical quantization framework.

Findings

Extended Dirac brackets enable quantization of dissipative systems.

Fractional formalism offers a systematic approach for nonconservative theories.

Potential to analyze gauge theories with second-class constraints more deeply.

Abstract

So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well known that the fractional formalism is a powerful alternative when treating dissipative problems. In this paper we propose a detailed way of attacking the issue using fractional calculus to construct an extension of the Dirac brackets in order to carry out the quantization of nonconservative theories through the standard canonical way. We believe that using the extended Dirac bracket definition it will be possible to analyze more deeply gauge theories starting with second-class systems.