Current Search: Hamiltonian systems (x)
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Title
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Hamiltonian Methods in the Quantization of Gauge Systems.
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Creator
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Vaulin, Ruslan, Florida Atlantic University, Miller, Warner A., Charles E. Schmidt College of Science, Department of Physics
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Abstract/Description
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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...
Show moreThe 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.
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Date Issued
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2006
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PURL
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http://purl.flvc.org/fau/fd/FA00000882
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Subject Headings
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Quantum field theory, Mathematical physics, Evolution equations, Nonlinear, Hamiltonian systems
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Format
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Document (PDF)
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Title
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Derivation of planar diffeomorphisms from Hamiltonians with a kick.
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Creator
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Barney, Zalmond C., Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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In this thesis we will discuss connections between Hamiltonian systems with a periodic kick and planar diffeomorphisms. After a brief overview of Hamiltonian theory we will focus, as an example, on derivations of the Hâenon map that can be obtained by considering kicked Hamiltonian systems. We will conclude with examples of Hâenon maps of interest.
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Date Issued
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2011
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PURL
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http://purl.flvc.org/FAU/3329833
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Subject Headings
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Mathematical physics, Differential equations, Partial, Hamiltonian systems, Algebra, Linear, Chaotic behavior in systems
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Format
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Document (PDF)
