Bicovariant Calculus in Quantum Theory and a Generalization of the Gauss Law

TL;DR

This paper develops a deformation of quantum algebra for Lie groups to quantum groups with bicovariant calculus, enabling a generalized Gauss law in quantum gauge theories.

Contribution

It introduces a new deformation of the algebra Fun(T^*G) to incorporate quantum groups with bicovariant calculus, extending gauge theory frameworks.

Findings

Constructed a deformation of Fun(T^*G) for quantum groups G_q.

Included current algebra of invariant one forms in the deformation.

Proposed a generalized Gauss law for quantum gauge theories.

Abstract

We construct a deformation of the quantum algebra Fun(T^*G) associated with Lie group G to the case where G is replaced by a quantum group G_q which has a bicovariant calculus. The deformation easily allows for the inclusion of the current algebra of left and right invariant one forms. We use it to examine a possible generalization of the Gauss law commutation relations for gauge theories based on G_q.