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Noncommutative Yang-Mills-Higgs actions from derivation-based differential calculus (2008)
| Venue: | arXiv:0804.3061, High Energy Physics - Theory (hep-th |
| Citations: | 22 - 13 self |
BibTeX
@INPROCEEDINGS{Cagnache08noncommutativeyang-mills-higgs,
author = {Eric Cagnache and Thierry Masson and Jean-christophe Wallet},
title = {Noncommutative Yang-Mills-Higgs actions from derivation-based differential calculus},
booktitle = {arXiv:0804.3061, High Energy Physics - Theory (hep-th},
year = {2008}
}
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Abstract
Derivations of a noncommutative algebra can be used to construct differential calculi, the so-called derivation-based differential calculi. We apply this framework to a version of the Moyal algebra M. We show that the differential calculus, generated by the maximal subalgebra of the derivation algebra of M that can be related to infinitesimal symplectomorphisms, gives rise to a natural construction of Yang-Mills-Higgs models on M and a natural interpretion of the covariant coordinates as Higgs fields. We also compare in detail the main mathematical properties characterizing the present situation to those specific of two other noncommutative geometries, namely the finite dimensional matrix algebra Mn(C) and the algebra of matrix valued functions C ∞ (M) ⊗ Mn(C). The UV/IR mixing problem of the resulting Yang-Mills-Higgs models is also discussed. Work supported by ANR grant NT05-3-43374 “GENOPHY”.
Keyphrases
derivation-based differential calculus noncommutative yang-mills-higgs action differential calculus yang-mills-higgs model finite dimensional matrix algebra mn moyal algebra infinitesimal symplectomorphisms higgs field natural construction present situation natural interpretion so-called derivation-based differential calculus derivation algebra main mathematical property noncommutative algebra noncommutative geometry maximal subalgebra anr grant nt05-3-43374 genophy uv ir
