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Dirac Spectra, Summation Formulae, and the Spectral Action


Teh, Kevin Kai-Wen (2013) Dirac Spectra, Summation Formulae, and the Spectral Action. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z545-KK47.


Noncommutative geometry is a source of particle physics models with matter Lagrangians coupled to gravity. One may associate to any noncommutative space (A, H, D) its spectral action, which is defined in terms of the Dirac spectrum of its Dirac operator D. When viewing a spin manifold as a noncommutative space, D is the usual Dirac operator. In this paper, we give nonperturbative computations of the spectral action for quotients of SU(2), Bieberbach manifolds, and SU(3) equipped with a variety of geometries. Along the way we will compute several Dirac spectra and refer to applications of this computation.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:noncommutative geometry; dirac operator; dirac spectrum; spectral action
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Marcolli, Matilde
Thesis Committee:
  • Marcolli, Matilde (chair)
  • Markovic, Vladimir
  • Venselaar, Joannes Jitse
  • Makarov, Nikolai G.
Defense Date:17 May 2013
Record Number:CaltechTHESIS:05082013-134706988
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7677
Deposited By: Kevin Teh
Deposited On:21 May 2013 18:19
Last Modified:28 Oct 2021 19:02

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