Pith. sign in

Generalized Fuzzy Torus and its Modular Properties

1 Pith paper cite this work. Polarity classification is still indexing.

1 Pith paper citing it
abstract

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 $\tau$. 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.

fields

math.QA 1

years

2019 1

verdicts

ACCEPT 1

representative citing papers

Finite spectral triples for the fuzzy torus

math.QA · 2019-08-19 · accept · novelty 6.0

A finite spectral triple for the fuzzy torus is constructed whose Dirac spectrum is the q-integer analogue of the commutative flat torus spectrum, for all four spin structures.

citing papers explorer

Showing 1 of 1 citing paper.

  • Finite spectral triples for the fuzzy torus math.QA · 2019-08-19 · accept · none · ref 7 · internal anchor

    A finite spectral triple for the fuzzy torus is constructed whose Dirac spectrum is the q-integer analogue of the commutative flat torus spectrum, for all four spin structures.