Ghost Loops are Indispensable in Unitary Gauge

TL;DR

This paper demonstrates that ghost loops are essential in the unitary gauge to cancel divergences and maintain gauge invariance, addressing a longstanding issue in quantum gauge field theory.

Contribution

It shows how to manage ultraviolet divergences in the unitary gauge, proving the necessity of ghost loops for gauge invariance and renormalization.

Findings

Ghost loops cancel divergences from vector mesons.

Physical amplitudes remain gauge invariant with ghost loops.

Handles ultraviolet divergences in the unitary gauge.

Abstract

It is conventionally taken for granted that the unitary gauge formulation of quantum gauge field theory has the advantage of preservation unitarity because only physical fields are involved but has the disadvantage of losing renormalizability because of severe ultraviolet divergences due to vector meson propagators. In this paper, we show how to handle the ultraviolet divergent loops so that the physical amplitudes remain gauge invariant. One of the consequences we arrive at is that ghost loops are needed to cancel the divergences due to vector mesons and to give gauge invariant physical amplitudes.