Generalized Fuzzy Torus and its Modular Properties

Autor(en)

Paul Schreivogl, Harold Steinacker

Abstrakt

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.

Organisation(en)

Mathematische Physik

Journal

Symmetry, Integrability and Geometry: Methods and Applications

Band

9

Anzahl der Seiten

23

ISSN

1815-0659

DOI

https://doi.org/10.3842/SIGMA.2013.060

Publikationsdatum

2013

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik, 103019 Mathematische Physik

Schlagwörter

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/92ae180b-2826-471b-845b-c601f3534e71