On the Effective Potential for Local Composite Operators

TL;DR

This paper demonstrates the usefulness of the effective potential for local composite operators in studying dynamical symmetry breaking, comparing different calculation methods in the GN and O(N) models.

Contribution

It introduces a method to calculate the effective potential for local composite operators using the CJT formalism with additional bare mass terms, and compares it with the auxiliary field approach.

Findings

Divergences in the effective potential match those in the CJT formalism.

The effective potential approach provides insights into dynamical symmetry breaking.

Comparison shows consistency between different computational methods.

Abstract

We show that the effective potential for local composite operators is a useful object in studing dynamical symmetry breaking by calculating the effective potential for the local composite operators $\bar{\psi} \psi$ and $\phi^2$ in the Gross-Neveu (GN) and O(N) models, respectively. Since the effective potential for local composite operators can be calculated by using the Cornwall-Jackiw-Tomboulis (CJT) effective potential in theory with additional bare mass terms, we show that divergences in the effective potential for local composite operators are the same as in the CJT effective potential. We compare the results obtained with the results give by the auxiliary field method.