The Path-Integral Approach to the N=2 Linear Sigma Model

TL;DR

This paper compares different methods of calculating the effective potential in the Euclidean N=2 linear sigma model, highlighting differences between the canonical and path-integral approaches in quantum field theory.

Contribution

It provides a detailed comparison of three methods for computing Green's functions and the effective potential in the N=2 linear sigma model, clarifying their relative advantages.

Findings

Different approaches yield varying effective potentials.

The path-integral and canonical methods can produce distinct results.

Discussion of the strengths and limitations of each method.

Abstract

In QFT the effective potential is an important tool to study symmetry breaking phenomena. It is known that, in some theories, the canonical approach and the path-integral approach yield different effective potentials. In this paper we investigate this for the Euclidean N=2 linear sigma model. Both the Green's functions and the effective potential will be computed in three different ways. The relative merits of the various approaches are discussed.