TL;DR
This paper explores gauge theories formulated on noncommutative spaces using the Moyal-Weyl product, highlighting the necessary modifications to symmetry structures, conservation laws, and field equations compared to classical gauge theories.
Contribution
It introduces a framework for gauge theories on noncommutative spaces with twisted Hopf algebra symmetry, extending traditional Lie algebra structures and analyzing resulting models.
Findings
Twisted Hopf algebra modifies gauge symmetry and conservation laws.
Extended enveloping algebra valued gauge fields are necessary.
Examples demonstrate consistency and novel features of the theories.
Abstract
Gauge theories are studied on a space of functions with the Moyal-Weyl product. The development of these ideas follows the differential geometry of the usual gauge theories, but several changes are forced upon us. The Leibniz rule has to be changed such that the theory is now based on a twisted Hopf algebra. Nevertheless, this twisted symmetry structure leads to conservation laws. The symmetry has to be extended from Lie algebra valued to enveloping algebra valued and new vector potentials have to be introduced. As usual, field equations are subjected to consistency conditions that restrict the possible models. Some examples are studied.
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