Aspects of the noncommutative torus
Publication Date
July 17, 2019
Creator
Abstract
In this thesis a class of finite real spectral triples for the geometry on a fuzzy torus is introduced. The geometries are shown to be related via an action of a general integral matrix. Each geometry is shown to have four real spectral triples corresponding to the four unique spin structures found on the 2-torus. The spectrum of the Dirac operator on each geometry, and spin structure, is calculated and shown to be the quantum integer analogues of the spectrum of the Dirac operator on the corresponding commutative 2-torus. The spectrum of the noncommutative Dirac operator is then shown to converge to the spectrum of the commutative Dirac operator as the algebra becomes commutative. Finally, an outline for the proof of a fuzzy torus converging to a commutative torus, via the defined Dirac operator, is presented.
Item Type
ethesis
Thesis Type
PhD
Supervisors
Subjects (LC)
Associated Schools / Departments
School of Mathematical Sciences (UK)
eprints ID
56288
UoN Repository URI
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Name
James Gaunt - Thesis.pdf
Type
Full-text
Description
Examined
Size
2.34 MB
Format
Adobe PDF
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