Mode dependent field renormalization and triviality

TL;DR

This paper critically examines a proposed field renormalization method in Phi4 theory, revealing it does not prevent triviality and results in an inconsistent effective potential in the continuum limit.

Contribution

It introduces and evaluates a zero momentum mode field renormalization approach, showing its limitations in addressing triviality in Phi4 theory.

Findings

The proposed renormalization leads to an infrared divergent effective action.

It does not prevent the emergence of massless particles in the broken phase.

The effective potential is inconsistent with the low energy limit of the effective action.

Abstract

We critically analyze the introduction of an independent zero momentum mode field renormalization for Phi4. It leads to an infrared divergent effective action. It does not achieve its purpose: triviality still gives massless particles in the broken phase in the continuum limit. It leads to an effective potential which is not the low energy limit of the effective action.