A Linear-confined Particle and the Dirac Equation

TL;DR

This paper presents a path integral quantization of a classical particle model with a linear AAD potential, resulting in a description equivalent to a Dirac particle, highlighting the role of internal variables and light cone constraints.

Contribution

It introduces a novel classical particle model with linear AAD potential and demonstrates its quantization leads to a Dirac particle description using path integrals.

Findings

Quantization yields a Dirac particle description.

Use of light cone constraints simplifies calculations.

Path integrals applied to a matrix form of transition amplitude.

Abstract

The model of a classical particle with the weak linear AAD potential is subjected to path integral quantization. The light cone constraints and peculiar properies of its internal variables permit to use in calculations commutative dynamics and apply path integrals for a matrix form of the transition amplitude. Quantization leads to description of a Dirac particle.