Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity

TL;DR

This paper applies stochastic quantization to a self-interacting nonminimal scalar field in curved spacetime, deriving quantum corrections and effective potential, and includes numerical simulations in three dimensions.

Contribution

It introduces a stochastic quantization approach combined with covariant methods to compute quantum effects for scalar fields in curved spacetime, extending previous results.

Findings

Reproduces known Euclidean correlation functions by Bunch and Parker.

Constructs the effective potential in curved spacetime up to first order in curvature.

Provides numerical simulations for three-dimensional cases.

Abstract

We employ stochastic quantization for a self-interacting nonminimal massive scalar field in curved spacetime. The covariant background field method and local momentum space representation are used to obtain the Euclidean correlation function and evaluate multi-loop quantum corrections through simultaneous expansions in the curvature tensor and its covariant derivatives and in the noise fields. The stochastic correlation function reproduces the well-known result by Bunch and Parker and is used to construct the effective potential in curved spacetime in an arbitrary dimension $D$ up to the first order in curvature. Furthermore, we present a sample of numerical simulations for $D=3$ in the first order in curvature.