The Effective Potential in the Massive $\phi_4^4$ Model

TL;DR

This paper extends the analysis of the effective potential in scalar quantum field theories to include the massive $\,\phi_4^4$ model, demonstrating its independence from the scalar field through renormalization group methods.

Contribution

It shows that the effective potential in the massive $\,\phi_4^4$ model is independent of the scalar field, extending previous results from massless models.

Findings

Effective potential is independent of the scalar field in the massive model.

Renormalization group equations confirm this independence.

Results unify understanding across massless and massive scalar theories.

Abstract

By applying the renormalization group equation, it has been shown that the effective potential $V$ in the massless $\phi_4^4$ model and in massless scalar quantum electrodynamics is independent of the scalar field. This analysis is extended here to the massive $\phi_4^4$ model, showing that the effective potential is independent of $\phi$ here as well.