Gauge Symmetries on $\theta$-Deformed Spaces

TL;DR

This paper develops a Hamiltonian framework for gauge symmetries on noncommutative $ heta$-deformed spaces, comparing star deformed and undeformed transformations, and offers a new interpretation of twisted coproducts.

Contribution

It introduces a Hamiltonian formulation for gauge symmetries on noncommutative spaces and clarifies the role of twisted coproducts in gauge transformations.

Findings

Identifies the gauge generator structure as identical in both cases

Highlights differences in graded Poisson brackets computation

Provides a novel interpretation of twisted coproducts

Abstract

A Hamiltonian formulation of gauge symmetries on noncommutative ($\theta$ deformed) spaces is discussed. Both cases- star deformed gauge transformation with normal coproduct and undeformed gauge transformation with twisted coproduct- are considered. While the structure of the gauge generator is identical in either case, there is a difference in the computation of the graded Poisson brackets that yield the gauge transformations. Our analysis provides a novel interpretation of the twisted coproduct for gauge transformations.