About the triviality of the higher derivative sector in the abelian Lee-Wick model

TL;DR

This paper demonstrates that the higher-derivative sector in the Abelian Lee-Wick model can be effectively removed through BRST symmetry, simplifying the theory and clarifying its physical degrees of freedom.

Contribution

It introduces a novel BRST-based method to eliminate the higher-derivative sector in the Abelian Lee-Wick model, clarifying the model's physical content.

Findings

Higher-derivative sector can be removed via BRST symmetry.

The Lee-Wick mass parameter is eliminated from the physical spectrum.

A new subsidiary condition based on higher-derivative invariance is proposed.

Abstract

Canonical quantization is reviewed here for the Abelian Lee-Wick model by using the Dirac constraints method, a Gupta-Bleuler-like prescription is implemented and the BRST charge operator for this model is built. New degrees of freedom associated to the (higher derivatives) Lee-Wick ghost are excluded from the (physical) space of observables by the imposition of a Piguet-Nielsen-type BRST-extended symmetry for the Lee-Wick mass term, removing the Lee-Wick mass parameter of the theory, which implies remove all the higher-derivative sector. In addition, another prescription based on a new subsidiary condition of invariance under a purely higher-derivative BRST-type new symmetry is proposed.