SU_q(n) Gauge Theory

TL;DR

This paper develops a gauge theory based on the quantum group SU_q(n), defining gauge transformations, potentials, and gauge-invariant relations within a classical spacetime framework, highlighting a non-trivial deformation.

Contribution

It introduces a consistent gauge theory with quantum group symmetries, extending classical gauge concepts to the quantum group setting with explicit transformation rules.

Findings

Gauge transformations lead to quantum-group consistent field strengths.

Gauge-invariant commutation relations are established.

The theory demonstrates a non-trivial deformation of classical gauge structures.

Abstract

A field theory with local transformations belonging to the quantum group SU_q(n) is defined on a classical spacetime, with gauge potentials belonging to a quantum Lie algebra. Gauge transformations are defined for the potentials which lead to the appropriate quantum-group transformations for field strengths and covariant derivatives, defined for all elements of SU_q(n) by means of the adjoint action. This guarantees a non-trivial deformation. Gauge-invariant commutation relations are identified.