Stochastic Quantization of Relativistic Theories

TL;DR

This paper extends stochastic quantization to relativistic theories by imposing a stochastic energy-momentum relation, deriving quantum corrections to spacetime geometry, and including massless particles, offering a new approach to quantum field theory on curved manifolds.

Contribution

It introduces a novel method for applying stochastic quantization to relativistic theories, incorporating quantum corrections and massless particles within a geometric framework.

Findings

Derived non-perturbative quantum corrections to the line element.

Extended stochastic quantization to massless scalar particles.

Showed how to impose relativistic restrictions via energy-momentum relations.

Abstract

It was shown recently that stochastic quantization can be made into a well defined quantization scheme on (pseudo-)Riemannian manifolds using second order differential geometry, which is an extension of the commonly used first order differential geometry. In this letter, we show that restrictions to relativistic theories can be obtained from this theory by imposing a stochastic energy-momentum relation. In the process, we derive non-perturbative quantum corrections to the line element as measured by scalar particles. Furthermore, we extend the framework of stochastic quantization to massless scalar particles.