Gauge theory on a space with linear Lie type fuzziness
Abstract
The U(1) gauge theory on a space with Lie type noncommutativity is constructed. The construction is based on the group of translation in Fourier space, which in contrast to space itself is commutative. In analogy with lattice gauge theory, the object playing the role of flux of field strength per plaquette, as well as the action, are constructed. It is observed that the theory, in comparison with ordinary U(1) gauge theory, has an extra gauge field component. This phenomena is reminiscent of similar ones in formulation of SU(N) gauge theory in space with canonical noncommutativity, and also appearance of gauge field component in discrete direction of Connes' construction of the Standard Model.
Keywords
Cite
@article{arxiv.1305.5410,
title = {Gauge theory on a space with linear Lie type fuzziness},
author = {M. Khorrami and A. H. Fatollahi and A. Shariati},
journal= {arXiv preprint arXiv:1305.5410},
year = {2023}
}
Comments
latex2e, 1+17 pages, no fig. arXiv admin note: substantial text overlap with arXiv:1208.2359. v2: font modification