Noncommutative Yang-Mills-Higgs actions from derivation-based differential calculus
| Autor: | Eric Cagnache, Thierry Masson, Jean-Christophe Wallet |
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| Přispěvatelé: | Laboratoire de Physique Théorique d'Orsay [Orsay] (LPT), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11) |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics Algebra and Number Theory 010308 nuclear & particles physics Differential form [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] FOS: Physical sciences Differential calculus Yang–Mills existence and mass gap Mathematical Physics (math-ph) 01 natural sciences Noncommutative geometry High Energy Physics - Theory (hep-th) Mixing (mathematics) Mathematics::Quantum Algebra 0103 physical sciences Covariant transformation Geometry and Topology Invariant (mathematics) 010306 general physics Differential (mathematics) Mathematical Physics Mathematics |
| Zdroj: | J. Noncommut. Geom. J. Noncommut. Geom., 2011, 5, pp.39-67 INSPIRE-HEP |
| Popis: | 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 ${\cal{M}}$. We show that the differential calculus, generated by the maximal subalgebra of the derivation algebra of ${\cal{M}}$ that can be related to infinitesimal symplectomorphisms, gives rise to a natural construction of Yang-Mills-Higgs models on ${\cal{M}}$ and a natural interpretation 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 $M_n({\mathbb{C}})$ and the algebra of matrix valued functions $C^\infty(M)\otimes M_n({\mathbb{C}})$. The UV/IR mixing problem of the resulting Yang-Mills-Higgs models is also discussed. 23 pages, 2 figures. Improved and enlarged version. Some references have been added and updated. Two subsections and a discussion on the appearence of Higgs fiels in noncommutative gauge theories have been added |
| Databáze: | OpenAIRE |
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