Generalized Gaussian Effective Potential: Low Dimensional Scalar Fields

TL;DR

This paper extends the Gaussian effective potential framework to low-dimensional scalar fields, incorporating two-loop corrections and discussing renormalization to improve understanding of quantum effects in these systems.

Contribution

It introduces a generalized Gaussian effective potential for 1D and 2D scalar fields, including two-loop corrections and renormalization procedures, advancing theoretical analysis.

Findings

Two-loop corrections significantly modify the effective potential.

Renormalization procedures are established for the generalized potential.

The approach enhances understanding of quantum effects in low-dimensional scalar fields.

Abstract

We study a generalization of the Gaussian effective potential for self-interacting scalar fields in one and two spatial dimensions. We compute the two-loop corrections and discuss the renormalization of the generalized Gaussian effective potential.