On the Composition of Gauge Structures

TL;DR

This paper introduces a novel method for composing two classical gauge structures into a single, fundamental gauge structure, highlighting the geometric origin of associated ghost fields and BRST variations.

Contribution

It presents a new formulation for combining gauge structures using related connections in product Lie algebra spaces, revealing irreducible components and their geometric properties.

Findings

Classifies composed gauge structures into trivial and irreducible types.

Identifies a pure irreducible component generating a super-space of ghosts.

Derives super-BRST laws from geometric principles.

Abstract

A formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is based on a pair of related connections that take their values in the product space of the corresponding Lie algebras. The curvature, the covariant exterior derivatives and the associated structural identities, all get contributions from both gauge groups. The various induced structures are classified into those whose composition is given just by trivial means, and those which possess an irreducible nature. The pure irreducible piece, in particular, generates a complete super-space of ghosts with an attendant set of super-BRST variation laws, both of which are purely of a geometrical origin.