Quantum Deformation of BRST Algebra

TL;DR

This paper explores the q-deformation of the BRST algebra, analyzing how the algebraic structure of ghost, matter, and gauge fields can be consistently modified using bicovariant differential calculus, including the properties of nilpotent operations.

Contribution

It introduces a consistent framework for q-deforming the BRST algebra, incorporating covariant commutation relations and the *-operation within bicovariant differential calculus.

Findings

Defined covariant commutation relations compatible with BRST and derivative operations

Established the consistency of *-operation in the q-deformed algebra

Demonstrated the nilpotency of BRST transformation in the deformed setting

Abstract

We investigate the $q$-deformation of the BRST algebra, the algebra of the ghost, matter and gauge fields on one spacetime point using the result of the bicovariant differential calculus. There are two nilpotent operations in the algebra, the BRST transformation $\brs$ and the derivative $d$. We show that one can define the covariant commutation relations among the fields and their derivatives consistently with these two operation as well as the $*$-operation, the antimultiplicative inner involution.