Quantization of spontaneously broken gauge theory based on the BFT-BFV Formalism

TL;DR

This paper presents a method to quantize the spontaneously broken U(1) Higgs model using the BFT and BFV formalisms, constructing gauge-invariant observables and deriving the gauge-symmetric Lagrangian.

Contribution

It introduces a systematic approach to quantize broken gauge theories via BFT-BFV formalisms, explicitly relating second class and first class quantities.

Findings

Constructed BFT physical fields and first class observables.

Derived the gauge-invariant Lagrangian from the broken symmetry Lagrangian.

Established exact form invariances between second and first class quantities.

Abstract

We quantize the spontaneously broken abelian U(1) Higgs model by using the improved BFT and BFV formalisms. We have constructed the BFT physical fields, and obtain the first class observables including the Hamiltonian in terms of these fields. We have also explicitly shown that there are exact form invariances between the second class and first class quantities. Then, according to the BFV formalism, we have derived the corresponding Lagrangian having U(1) gauge symmetry. We also discuss at the classical level how one easily gets the first class Lagrangian from the symmetry-broken second class Lagrangian.