BFV quantization and BRST symmetries of the gauge invariant fourth-order Pais-Uhlenbeck oscillator

TL;DR

This paper develops a BRST quantization framework for the fourth-order Pais-Uhlenbeck oscillator, introducing constraints and gauge symmetries to facilitate its quantum description.

Contribution

It applies the BFV-BRST formalism to a higher-derivative oscillator, using BFFT conversion to handle second-class constraints and establishing gauge invariance.

Findings

Successfully constructed BRST charge and transformations.

Connected different gauge choices via finite field-dependent BRST transformations.

Provided a consistent quantum description of the Pais-Uhlenbeck oscillator.

Abstract

We perform the BFV-BRST quantization of the fourth-order Pais-Uhlenbeck oscillator (PUO). We show that although the PUO is not naturally constrained in the sense of Dirac-Bergmann, it is possible to profit from the introduction of suitable constraints in phase space in order to obtain a proper BRST invariant quantum system. Starting from its second-class constrained system description, we use the BFFT conversional approach to obtain first-class constraints as gauge symmetry generators. After the Abelianization of the constraints, we obtain the conserved BRST charge, the corresponding BRST transformations and proceed further to the BFV functional quantization of the model. We show that different possible gauge choices can be connected by finite field-dependent BRST transformations.