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Hamiltonian Methods in the Quantization of Gauge Systems

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Date Issued:
2006
Summary:
The new formalism for quantization of gauge systems based on the concept of the dynamical Hamiltonian recently introduced as a basis for the canonical theory of quantum gravity was considered in the context of general gauge theories. This and other Hamiltonian methods, that include Dirac's theory of extended Hamiltonian and the Hamiltonian reduction formalism were critically examined. It was established that the classical theories of constrained gauge systems formulated within the framework of either of the approaches are equivalent. The central to the proof of equivalence was the fact that the gauge symmetries resuIt in the constraints of the first class in Dirac's terminology that Iead to redundancy of equations of motion for some of the canonica variables. Nevertheless, analysis of the quantum theories showed that in general, the quantum theory of the dynamical Hamiltonian is inequivalent to those of the extended Hamiltonian and the Hamiltonian reduction. The new method of quantization was applied to a number of gauge systems, including the theory of relativistic particle, the Bianchi type IX cosmological model and spinor electrodynamics along side with the traditional methods of quantization. In all of the cases considered the quantum theory of the dynamical Hamiltonian was found to be well-defined and to possess the appropriate classical limit. In particular, the quantization procedure for the Bianchi type IX cosmological spacetime did not run into any of the known problems with quantizing the theory of General Relativity. On the other hand, in the case of the quantum electrodynamics the dynamical Hamiltonian approach led to the quantum theory with the modified self-interaction in the matter sector. The possible consequence of this for the quantization of the full theory of General Relativity including the matter fields are discussed.
Title: Hamiltonian Methods in the Quantization of Gauge Systems.
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Name(s): Vaulin, Ruslan
Florida Atlantic University, Degree grantor
Miller, Warner A., Thesis advisor
Charles E. Schmidt College of Science
Department of Physics
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2006
Date Issued: 2006
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 140 p.
Language(s): English
Summary: The new formalism for quantization of gauge systems based on the concept of the dynamical Hamiltonian recently introduced as a basis for the canonical theory of quantum gravity was considered in the context of general gauge theories. This and other Hamiltonian methods, that include Dirac's theory of extended Hamiltonian and the Hamiltonian reduction formalism were critically examined. It was established that the classical theories of constrained gauge systems formulated within the framework of either of the approaches are equivalent. The central to the proof of equivalence was the fact that the gauge symmetries resuIt in the constraints of the first class in Dirac's terminology that Iead to redundancy of equations of motion for some of the canonica variables. Nevertheless, analysis of the quantum theories showed that in general, the quantum theory of the dynamical Hamiltonian is inequivalent to those of the extended Hamiltonian and the Hamiltonian reduction. The new method of quantization was applied to a number of gauge systems, including the theory of relativistic particle, the Bianchi type IX cosmological model and spinor electrodynamics along side with the traditional methods of quantization. In all of the cases considered the quantum theory of the dynamical Hamiltonian was found to be well-defined and to possess the appropriate classical limit. In particular, the quantization procedure for the Bianchi type IX cosmological spacetime did not run into any of the known problems with quantizing the theory of General Relativity. On the other hand, in the case of the quantum electrodynamics the dynamical Hamiltonian approach led to the quantum theory with the modified self-interaction in the matter sector. The possible consequence of this for the quantization of the full theory of General Relativity including the matter fields are discussed.
Identifier: FA00000882 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2006.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Charles E. Schmidt College of Science
Subject(s): Quantum field theory
Mathematical physics
Evolution equations, Nonlinear
Hamiltonian systems
Held by: Florida Atlantic University Libraries
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00000882
Sublocation: Digital Library
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.