BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry

TL;DR

This paper develops a BRST invariant formulation of spontaneously broken gauge theories within a generalized differential geometry framework on discrete spaces, extending noncommutative geometry approaches to include gauge fixing and BRST symmetry.

Contribution

It introduces a BRST invariant Lagrangian formulation of broken gauge theories using generalized differential geometry on discrete spaces, expanding the geometric understanding of symmetry breaking.

Findings

Constructed BRST invariant Lagrangian with gauge fixing

Extended differential geometry to discrete spaces for gauge theories

Connected noncommutative geometry with BRST symmetry in gauge theories

Abstract

Noncommutative geometry(NCG) on the discrete space successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory, in which the Higgs boson field is regarded as a kind of gauge field on the discrete space. We could construct the generalized differential geometry(GDG) on the discrete space $M_4\times Z_N$ which is very close to NCG in case of $M_4\times Z_2$. GDG is a direct generalization of the differential geometry on the ordinary manifold into the discrete one. In this paper, we attempt to construct the BRST invariant formulation of spontaneously broken gauge theory based on GDG and obtain the BRST invariant Lagrangian with the t'Hooft-Feynman gauge fixing term.