Gauge transformations for twisted spectral triples

It is extended to twisted spectral triples the fluctuations of the metric as bounded perturbations of the Dirac operator that arises when a spectral triple is exported between Morita equivalent algebras, as well as gauge transformations which are obtained by the action of the unitary endomorphisms o...

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Vydáno v:Letters in mathematical physics Ročník 108; číslo 12; s. 2589 - 2626
Hlavní autoři: Landi, Giovanni, Martinetti, Pierre
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.12.2018
Springer Nature B.V
Témata:
Complex Systems
Elementary particles
Equivalence
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Riemann manifold
Spectra
Standard model (particle physics)
Theoretical
Transformations
Variations
Morita equivalence
Secondary 16D90
Primary 58B34
Connes standard model
81T75
Noncommutative geometry
Algebra authomorphisms
Twisted real spectral triples
Gauge transformations
ISSN:0377-9017, 1573-0530
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Shrnutí:It is extended to twisted spectral triples the fluctuations of the metric as bounded perturbations of the Dirac operator that arises when a spectral triple is exported between Morita equivalent algebras, as well as gauge transformations which are obtained by the action of the unitary endomorphisms of the module implementing the Morita equivalence. It is firstly shown that the twisted-gauged Dirac operators, previously introduced to generate an extra scalar field in the spectral description of the standard model of elementary particles, in fact follow from Morita equivalence between twisted spectral triples. The law of transformation of the gauge potentials turns out to be twisted in a natural way. In contrast with the non-twisted case, twisted fluctuations do not necessarily preserve the self-adjointness of the Dirac operator. For a self-Morita equivalence, conditions are obtained in order to maintain self-adjointness that are solved explicitly for the minimal twist of a Riemannian manifold.
Bibliografie:ObjectType-Article-1
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ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-018-1099-3