Generalized Fuzzy Torus and its Modular Properties

Generalized Fuzzy Torus and its Modular Properties

We consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy...

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Bibliographic Details
Main Authors: Paul Schreivogl, Harold Steinacker
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2013-10-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
fuzzy spaces
noncommutative geometry
matrix models
Online Access:http://dx.doi.org/10.3842/SIGMA.2013.060
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spelling doaj-c92c5466f5a34a4e844df26b54c6756b2020-11-24T22:51:26ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592013-10-01906010.3842/SIGMA.2013.060Generalized Fuzzy Torus and its Modular PropertiesPaul SchreivoglHarold SteinackerWe consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy torus can be used to approximate a generic commutative torus represented by two generic vectors in the complex plane, with generic modular parameter τ. The effective classical geometry and the spectrum of the Laplacian are correctly reproduced in the limit. The spectrum of a matrix Dirac operator is also computed.http://dx.doi.org/10.3842/SIGMA.2013.060fuzzy spacesnoncommutative geometrymatrix models
collection DOAJ
language English
format Article
sources DOAJ
author Paul Schreivogl
Harold Steinacker
spellingShingle Paul Schreivogl
Harold Steinacker
Generalized Fuzzy Torus and its Modular Properties
Symmetry, Integrability and Geometry: Methods and Applications
fuzzy spaces
noncommutative geometry
matrix models
author_facet Paul Schreivogl
Harold Steinacker
author_sort Paul Schreivogl
title Generalized Fuzzy Torus and its Modular Properties
title_short Generalized Fuzzy Torus and its Modular Properties
title_full Generalized Fuzzy Torus and its Modular Properties
title_fullStr Generalized Fuzzy Torus and its Modular Properties
title_full_unstemmed Generalized Fuzzy Torus and its Modular Properties
title_sort generalized fuzzy torus and its modular properties
publisher National Academy of Science of Ukraine
series Symmetry, Integrability and Geometry: Methods and Applications
issn 1815-0659
publishDate 2013-10-01
description We consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy torus can be used to approximate a generic commutative torus represented by two generic vectors in the complex plane, with generic modular parameter τ. The effective classical geometry and the spectrum of the Laplacian are correctly reproduced in the limit. The spectrum of a matrix Dirac operator is also computed.
topic fuzzy spaces
noncommutative geometry
matrix models
url http://dx.doi.org/10.3842/SIGMA.2013.060
work_keys_str_mv AT paulschreivogl generalizedfuzzytorusanditsmodularproperties
AT haroldsteinacker generalizedfuzzytorusanditsmodularproperties
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