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 Simplical matter in discrete and quantum spacetimes.

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Type of Resource: text

Genre: Electronic Thesis or Dissertation

Issuance: monographic

Date Issued: 2009

Publisher: Florida Atlantic University

Physical Form: electronic

Extent: viii, 95 p. : ill. (some col.).

Language(s): English

Summary: A discrete formalism for General Relativity was introduced in 1961 by Tulio Regge in the form of a piecewise-linear manifold as an approximation to (pseudo-)Riemannian manifolds. This formalism, known as Regge Calculus, has primarily been used to study vacuum spacetimes as both an approximation for classical General Relativity and as a framework for quantum gravity. However, there has been no consistent effort to include arbitrary non-gravitational sources into Regge Calculus or examine the structural details of how this is done. This manuscript explores the underlying framework of Regge Calculus in an effort elucidate the structural properties of the lattice geometry most useful for incorporating particles and fields. Correspondingly, we first derive the contracted Bianchi identity as a guide towards understanding how particles and fields can be coupled to the lattice so as to automatically ensure conservation of source. In doing so, we derive a Kirchhoff-like conservation principle that identifies the flow of energy and momentum as a flux through the circumcentric dual boundaries. This circuit construction arises naturally from the topological structure suggested by the contracted Bianchi identity. Using the results of the contracted Bianchi identity we explore the generic properties of the local topology in Regge Calculus for arbitrary triangulations and suggest a first-principles definition that is consistent with the inclusion of source. This prescription for extending vacuum Regge Calculus is sufficiently general to be applicable to other approaches to discrete quantum gravity. We discuss how these findings bear on a quantized theory of gravity in which the coupling to source provides a physical interpretation for the approximate invariance principles of the discrete theory.

Identifier: 318641665 (oclc), 186691 (digitool), FADT186691 (IID), fau:2906 (fedora)

Note(s): by Jonathan Ryan McDonald.Vita.Thesis (Ph.D.)--Florida Atlantic University, 2009.Includes bibliography.Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

Subject(s): Tulio, ReggeSpecial relativity (Physics)Space and timeDistribution (Probability theory)Global differential geometryQuantum field theoryMathematical physics

Held by: FBoU FAUER

Persistent Link to This Record:

Owner Institution: FAU

Autor: McDonald, Jonathan Ryan.



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