Auxiliary representations of Lie algebras and the BRST constructions

TL;DR

This paper explores a BRST-based method for constructing auxiliary representations of Lie algebras, addressing the non-hermiticity of the BRST charge by introducing a kernel operator, which is proven to exist universally.

Contribution

It introduces a novel approach to construct auxiliary Lie algebra representations within the BRST framework, resolving hermiticity issues with a new kernel operator.

Findings

BRST charge is non-hermitian in this context

A kernel operator can restore hermiticity in the scalar product

Existence of the kernel operator is proven for all Lie algebras

Abstract

The method of construction of auxiliary representations for a given Lie algebra is discussed in the framework of the BRST approach. The corresponding BRST charge turns out to be non -- hermitian. This problem is solved by the introduction of the additional kernel operator in the definition of the scalar product in the Fock space. The existence of the kernel operator is proven for any Lie algebra.