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Title: Spin-foam dynamics of general relativity.
Creator: Chaharsough Shirazi, Atousa, Engle, Jonathan S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: In this dissertation the dynamics of general relativity is studied via the spin-foam approach to quantum gravity. Spin-foams are a proposal to compute a transition amplitude from a triangulated space-time manifold for the evolution of quantum 3d geometry via path integral. Any path integral formulation of a quantum theory has two important parts, the measure factor and a phase part. The correct measure factor is obtained by careful canonical analysis at the continuum level. The basic...
Show moreIn this dissertation the dynamics of general relativity is studied via the spin-foam approach to quantum gravity. Spin-foams are a proposal to compute a transition amplitude from a triangulated space-time manifold for the evolution of quantum 3d geometry via path integral. Any path integral formulation of a quantum theory has two important parts, the measure factor and a phase part. The correct measure factor is obtained by careful canonical analysis at the continuum level. The basic variables in the Plebanski-Holst formulation of gravity from which spin-foam is derived are a Lorentz connection and a Lorentz-algebra valued two-form, called the Plebanski two-form. However, in the final spin-foam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski two-form alone. The spin-foam sum is therefore a discretized version of a Plebanski-Holst path integral in which only the Plebanski two-form appears, and in which the conne ction degrees of freedom have been integrated out. Calculating the measure factor for Plebanksi Holst formulation without the connection degrees of freedom is one of the aims of this dissertation. This analysis is at the continuum level and in order to be implemented in spin-foams one needs to properly discretize and quantize this measure factor. The correct phase is determined by semi-classical behavior. In asymptotic analysis of the Engle-Pereira-Rovelli-Livine spin-foam model, due to the inclusion of more than the usual gravitational sector, more than the usual Regge term appears in the asymptotics of the vertex amplitude. As a consequence, solutions to the classical equations of motion of GR fail to dominate in the semi-classical limit. One solution to this problem has been proposed in which one quantum mechanically imposes restriction to a single gravitational sector, yielding what has been called the “proper” spin-foam model. However, this revised model of quantum gravity, like any proposal for a theory of quantum gravity, must pass certain tests. In the regime of small curvature, one expects a given model of quantum gravity to reproduce the predictions of the linearized theory. As a consistency check we calculate the graviton two-point function predicted by the Lorentzian proper vertex and examine its semiclassical limit.
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Date Issued: 2015
PURL: http://purl.flvc.org/fau/fd/FA00004488, http://purl.flvc.org/fau/fd/FA00004488
Subject Headings: General relativity (Physics), Gravitation, Mass (Physics), Mathematical physics, Quantum gravity, Quantum theory
Format: Document (PDF)

Title: Elliptic curves: identity-based signing and quantum arithmetic.
Creator: Budhathoki, Parshuram, Steinwandt, Rainer, Eisenbarth, Thomas, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Pairing-friendly curves and elliptic curves with a trapdoor for the discrete logarithm problem are versatile tools in the design of cryptographic protocols. We show that curves having both properties enable a deterministic identity-based signing with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon proposed an identity-based signature scheme along with a provable security reduction. We propose a modification of their scheme with several performance benefits. In...
Show morePairing-friendly curves and elliptic curves with a trapdoor for the discrete logarithm problem are versatile tools in the design of cryptographic protocols. We show that curves having both properties enable a deterministic identity-based signing with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon proposed an identity-based signature scheme along with a provable security reduction. We propose a modification of their scheme with several performance benefits. In addition to faster signing, for batch signing the signature size can be reduced, and if multiple signatures for the same identity need to be verified, the verification can be accelerated. Neither the signing nor the verification algorithm rely on the availability of a (pseudo)random generator, and we give a provable security reduction in the random oracle model to the (`-)Strong Diffie-Hellman problem. Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor’s algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. Our Python software generates circuit descriptions that, without increasing the number of qubits or T-depth, involve less than 39% of the number of T-gates in the best previous construction. The software also optimizes the (CNOT) depth for F2-linear operations by means of suitable graph colorings.
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Date Issued: 2014
PURL: http://purl.flvc.org/fau/fd/FA00004182, http://purl.flvc.org/fau/fd/FA00004182
Subject Headings: Coding theory, Computer network protocols, Computer networks -- Security measures, Data encryption (Computer science), Mathematical physics, Number theory -- Data processing
Format: Document (PDF)

Title: Synchronization and phase dynamics of oscillating foils.
Creator: Finkel, Cyndee L., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: In this work, a two-dimensional model representing the vortices that animals produce, when they are flying/swimming, was constructed. A D{shaped cylinder and an oscillating airfoil were used to mimic these body{shed and wing{generated vortices, respectively. The parameters chosen are based on the Reynolds numbers similar to that which is observed in nature (104). In order to imitate the motion of ying/swimming, the entire system was suspended into a water channel from frictionless air...
Show moreIn this work, a two-dimensional model representing the vortices that animals produce, when they are flying/swimming, was constructed. A D{shaped cylinder and an oscillating airfoil were used to mimic these body{shed and wing{generated vortices, respectively. The parameters chosen are based on the Reynolds numbers similar to that which is observed in nature (104). In order to imitate the motion of ying/swimming, the entire system was suspended into a water channel from frictionless air{bearings. The position of the apparatus in the channel was regulated with a linear, closed loop PI controller. Thrust/drag forces were measured with strain gauges and particle image velocimetry (PIV) was used to examine the wake structure that develops. The Strouhal number of the oscillating airfoil was compared to the values observed in nature as the system transitions between the accelerated and steady states... As suggested by previous work, this self-regulation is a result of a limit cycle process that stems from nonlinear periodic oscillations. The limit cycles were used to examine the synchronous conditions due to the coupling of the foil and wake vortices. Noise is a factor that can mask details of the synchronization. In order to control its effect, we study the locking conditions using an analytic technique that only considers the phases.. The results suggest that Strouhal number selection in steady forward natural swimming and flying is the result of a limit cycle process and not actively controlled by an organism. An implication of this is that only relatively simple sensory and control hardware may be necessary to control the steady forward motion of man-made biomimetically propelled vehicles.
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Date Issued: 2013
PURL: http://purl.flvc.org/fcla/dt/3362333
Subject Headings: Mathematical physics, Fluid dynamics, Unsteady flow (Fluid dynamics), Aerofoils, Aerodynamics
Format: Document (PDF)

Title: Coset intersection problem and application to 3-nets.
Creator: Pace, Nicola, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all...
Show moreIn a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all possible sporadic examples. If p is larger than the order of the group, the same classification holds true apart from three possible exceptions: Alt4, Sym4 and Alt5.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3355866
Subject Headings: Finite fields (Algebra), Mathematical physics, Field theory (Physics), Curves, Algebraic
Format: Document (PDF)

Title: A study of divisors and algebras on a double cover of the affine plane.
Creator: Bulj, Djordje., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: An algebraic surface defined by an equation of the form z2 = (x+a1y) ... (x + any) (x - 1) is studied, from both an algebraic and geometric point of view. It is shown that the surface is rational and contains a singular point which is nonrational. The class group of Weil divisors is computed and the Brauer group of Azumaya algebras is studied. Viewing the surface as a cyclic cover of the affine plane, all of the terms in the cohomology sequence of Chase, Harrison and Roseberg are computed.
Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3355618
Subject Headings: Algebraic number theory, Geometry, Data processing, Noncommutative differential geometry, Mathematical physics, Curves, Algebraic, Commutative rings
Format: Document (PDF)

Title: Derivation of planar diffeomorphisms from Hamiltonians with a kick.
Creator: Barney, Zalmond C., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: 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.
Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3329833
Subject Headings: Mathematical physics, Differential equations, Partial, Hamiltonian systems, Algebra, Linear, Chaotic behavior in systems
Format: Document (PDF)

Title: Gravitational signature of core-collapse supernova results of CHIMERA simulations.
Creator: Yakunin, Konstantin., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: Core-collapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of...
Show moreCore-collapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of the prime sources of gravitational waves for interferometric detectors. Gravitational waves can give us access to the electromagnetically hidden compact inner core of supernovae. They will provide valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. Detection of GW signals and analysis of the observations will require realistic signal predi ctions from the non-parameterized relativistic numerical simulations of CCSN. This dissertation presents the gravitational wave signature of core-collapse v supernovae. Previous studies have considered either parametric models or nonexploding models of CCSN. This work presents complete waveforms, through the explosion phase, based on first-principles models for the first time. We performed 2D simulations of CCSN using the CHIMERA code for 12, 15, and 25M non-rotating progenitors. CHIMERA incorporates most of the criteria for realistic core-collapse modeling, such as multi-frequency neutrino transport coupled with relativistic hydrodynamics, eective GR potential, nuclear reaction network, and an industry-standard equation of state., Based on the results of our simulations, I produced the most realistic gravitational waveforms including all postbounce phases of core-collapse supernovae: the prompt convection, the stationary accretion shock instability, and the corresponding explosion. Additionally, the tracer particles applied in the analysis of the GW signal reveal the origin of low-frequency component in the prompt part of gravitational waveform. Analysis of detectability of the GW signature from a Galactic event shows that the signal is within the band-pass of current and future GW observatories such as AdvLIGO, advanced Virgo, and LCGT.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3322512
Subject Headings: Mathematical physics, Continuum mechanics, Supernovae, Mathematical models
Format: Document (PDF)

Title: Simplicial matter in discrete and quantum spacetimes.
Creator: McDonald, Jonathan Ryan., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: 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...
Show moreA 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.
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Date Issued: 2009
PURL: http://purl.flvc.org/FAU/186691
Subject Headings: Special relativity (Physics), Space and time, Distribution (Probability theory), Global differential geometry, Quantum field theory, Mathematical physics
Format: Document (PDF)

Title: First-principles study of metastable phases and structural anomalies of Fe, Al, Zn, and Cd under pressure.
Creator: Apostol, Florin., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: Stable and metastable phases of Fe and Al and structural anomalies of Zn and Cd have been studied by epitaxial Bain path (EBP) and minimum path (MNP) first-principles procedures, based on finding equilibrium structures from minimizing the Gibbs free energy G with respect to structure at a given hydrostatic pressure p and temperature T . The main accomplishments are as follows. (1) This dissertation illustrates the effectiveness of the MNP procedure for finding stable and metastable phases of...
Show moreStable and metastable phases of Fe and Al and structural anomalies of Zn and Cd have been studied by epitaxial Bain path (EBP) and minimum path (MNP) first-principles procedures, based on finding equilibrium structures from minimizing the Gibbs free energy G with respect to structure at a given hydrostatic pressure p and temperature T . The main accomplishments are as follows. (1) This dissertation illustrates the effectiveness of the MNP procedure for finding stable and metastable phases of an element by studying four Bravais phases of Fe including body-centered tetragonal (bct), body-centered cubic (bcc), face-centered cubic (fcc) and rhombohedral (rh) phases. The determination of absolute stability using MNP is new; MNP finds all the elastic constants cjj of a given state and the eigenvalues of the elastic constants matrix, which determine the absolute stability of the state., (2) We have extended our search for stable and metastable phases from zero temperature to finite temperature, which requires the calculations of the Debye temperature Od from cjj in the case of no symmetry. The Debye theory is modified by introducing a parameter B2 that gives the fraction of the full Debye zero-point energy possessed by the actual dispersive mode frequencies. The value of the lattice parameter of fcc Al at low temperatures,a(T) , is shown to be accurately determined by the modified Debye theory of lattice vibrations and first-principles total energy band calculations with the MNP procedure. (3) The existence of structural anomalies in hcp Zn and Cd has been shown from first-principles total-energy calculations using WIEN2k with the EBP procedure., Evaluation of the pressure dependence of various elastic quantities which are much more sensitive to the anomaly shows that the anomalies in hcp Zn and hcp Cd exist over a considerable range of pressure; several abrupt changes in the electron distribution are thereby indicated in that pressure range. (4) Calculations on the zone-center transverse optical phonon frequencies Vto(p) of hcp Zn, which found oscillatory behavior of Vto(p) in the pressure range of the anomalies, support the conclusions made in (3) on the structural anomalies. Based on this dissertation research four papers have been published in refereed journals.
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Date Issued: 2008
PURL: http://purl.flvc.org/FAU/186334
Subject Headings: Epitaxy, Mathematical physics, Metals, Electric properties, Phase transformation (Statistical physics)
Format: Document (PDF)

Title: Subjecting the CHIMERA supernova code to two hydrodynamic test problems, (i) Riemann problem and (ii) Point blast explosion.
Creator: Ahsan, Abu Salah M., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: A Shock wave as represented by the Riemann problem and a Point-blast explosion are two key phenomena involved in a supernova explosion. Any hydrocode used to simulate supernovae should be subjected to tests consisting of the Riemann problem and the Point-blast explosion. L. I. Sedov's solution of Point-blast explosion and Gary A. Sod's solution of a Riemann problem have been re-derived here from one dimensional fluid dynamics equations . Both these problems have been solved by using the idea...
Show moreA Shock wave as represented by the Riemann problem and a Point-blast explosion are two key phenomena involved in a supernova explosion. Any hydrocode used to simulate supernovae should be subjected to tests consisting of the Riemann problem and the Point-blast explosion. L. I. Sedov's solution of Point-blast explosion and Gary A. Sod's solution of a Riemann problem have been re-derived here from one dimensional fluid dynamics equations . Both these problems have been solved by using the idea of Self-similarity and Dimensional analysis. The main focus of my research was to subject the CHIMERA supernova code to these two hydrodynamic tests. Results of CHIMERA code for both the blast wave and Riemann problem have then been tested by comparing with the results of the analytic solution.
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Date Issued: 2008
PURL: http://purl.flvc.org/FAU/172665
Subject Headings: Mathematical physics, Continuum mechanics, Number theory, Supernovae, Data processing, Shock waves, Fluid dynamics
Format: Document (PDF)

Title: Structured flows on manifolds: distributed functional architectures.
Creator: Pillai, Ajay S., Florida Atlantic University, Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
Abstract/Description: Despite the high-dimensional nature of the nervous system, humans produce low-dimensional cognitive and behavioral dynamics. How high-dimensional networks with complex connectivity give rise to functionally meaningful dynamics is not well understood. How does a neural network encode function? How can functional dynamics be systematically obtained from networks? There exist few frameworks in the current literature that answer these questions satisfactorily. In this dissertation I propose a...
Show moreDespite the high-dimensional nature of the nervous system, humans produce low-dimensional cognitive and behavioral dynamics. How high-dimensional networks with complex connectivity give rise to functionally meaningful dynamics is not well understood. How does a neural network encode function? How can functional dynamics be systematically obtained from networks? There exist few frameworks in the current literature that answer these questions satisfactorily. In this dissertation I propose a general theoretical framework entitled 'Structured Flows on Manifolds' and its underlying mathematical basis. The framework is based on the principles of non-linear dynamical systems and Synergetics and can be used to understand how high-dimensional systems that exhibit multiple time-scale behavior can produce low-dimensional dynamics. Low-dimensional functional dynamics arises as a result of the timescale separation of the systems component's dynamics. The low-dimensional space in which the functi onal dynamics occurs is regarded as a manifold onto which the entire systems dynamics collapses. For the duration of the function the system will stay on the manifold and evolve along the manifold. From a network perspective the manifold is viewed as the product of the interactions of the network nodes. The subsequent flows on the manifold are a result of the asymmetries of network's interactions. A distributed functional architecture based on this perspective is presented. Within this distributed functional architecture, issues related to networks such as flexibility, redundancy and robustness of the network's dynamics are addressed. Flexibility in networks is demonstrated by showing how the same network can produce different types of dynamics as a function of the asymmetrical coupling between nodes. Redundancy can be achieved by systematically creating different networks that exhibit the same dynamics. The framework is also used to systematically probe the effects of lesion, (removal of nodes) on network dynamics. It is also shown how low-dimensional functional dynamics can be obtained from firing-rate neuron models by placing biologically realistic constraints on the coupling. Finally the theoretical framework is applied to real data. Using the structured flows on manifolds approach we quantify team performance and team coordination and develop objective measures of team performance based on skill level.
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Date Issued: 2008
PURL: http://purl.flvc.org/FAU/77649
Subject Headings: Manifolds (Mathematics), Differentiable dynamical systems, Mathematical physics
Format: Document (PDF)

Title: Neural field dynamics under vari ation of local and global connectivity and finite t ransmission speeds.
Creator: Qubbaj, Murad R., Florida Atlantic University, Jirsa, Viktor K., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: Spatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in part icular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, the st ability of the steady state activity of a neural field as a fun ction of its connectivity is investigated. The variation of the connectivity is operationalized through manipulation of a heterogeneous two-point connection embedded into the otherwise homogeneous...
Show moreSpatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in part icular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, the st ability of the steady state activity of a neural field as a fun ction of its connectivity is investigated. The variation of the connectivity is operationalized through manipulation of a heterogeneous two-point connection embedded into the otherwise homogeneous connectivity matrix and by variation of connectivity strength and transmission speed. A detailed discussion of the example of the real Ginzburg-Land au equation with an embedded two-point heterogeneous connection in addition to the homogeneous coupling due to the diffusion term is performed. The system is reduced to a set of delay differential equations and the stability di agrams as a function of the time delay and the local and global coupling strengths are computed. The major finding is that the stability of the heterogeneously connected elements with a well-defined velocity defines a lower bound for the stabil ity of the entire system . Diffusion and velocity dispersion always result in increased stability. Various other local architectures represented by exponentially decaying connectivity fun ctions are also discussed. The analysis shows that developmental changes such as the myelination of the cortical large-scale fib er system generally result in the stabilization of steady state activity via oscillatory instabilities independent of the local connectivity. Non-oscillatory (Turing) instabilities are shown to be independent of any influences of time delay.
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Date Issued: 2007
PURL: http://purl.flvc.org/fau/fd/FA00000873
Subject Headings: Mathematical physics, Connections (Mathematics), Superconductivity--Mathematics, Neural networks (Computer science)
Format: Document (PDF)

Title: Hamiltonian Methods in the Quantization of Gauge Systems.
Creator: Vaulin, Ruslan, Florida Atlantic University, Miller, Warner A., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: 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: 2006
PURL: http://purl.flvc.org/fau/fd/FA00000882
Subject Headings: Quantum field theory, Mathematical physics, Evolution equations, Nonlinear, Hamiltonian systems
Format: Document (PDF)

Continuum mechanics (2)	+ -
Curves, Algebraic (2)	+ -
Data processing (2)	+ -
Fluid dynamics (2)	+ -
Hamiltonian systems (2)	+ -

Quantum field theory (2)	+ -
Supernovae (2)	+ -
Aerodynamics (1)	+ -
Aerofoils (1)	+ -
Algebra, Linear (1)	+ -
Algebraic number theory (1)	+ -
Chaotic behavior in systems (1)	+ -
Coding theory (1)	+ -
Commutative rings (1)	+ -
Computer network protocols (1)	+ -
Computer networks -- Security measures (1)	+ -
Connections (Mathematics) (1)	+ -
Data encryption (Computer science) (1)	+ -
Differentiable dynamical systems (1)	+ -
Differential equations, Partial (1)	+ -
Distribution (Probability theory) (1)	+ -
Electric properties (1)	+ -
Epitaxy (1)	+ -
Evolution equations, Nonlinear (1)	+ -
Field theory (Physics) (1)	+ -
Finite fields (Algebra) (1)	+ -
General relativity (Physics) (1)	+ -
Geometry (1)	+ -
Global differential geometry (1)	+ -

Department of Physics (8)	+ -
Florida Atlantic University (6)	+ -
Department of Mathematical Sciences (4)	+ -
Ahsan, Abu Salah M. (1)	+ -
Apostol, Florin. (1)	+ -

Barney, Zalmond C. (1)	+ -
Budhathoki, Parshuram (1)	+ -
Bulj, Djordje. (1)	+ -
Center for Complex Systems and Brain Sciences (1)	+ -
Chaharsough Shirazi, Atousa (1)	+ -
Eisenbarth, Thomas (1)	+ -
Engle, Jonathan S. (1)	+ -
Finkel, Cyndee L. (1)	+ -
Jirsa, Viktor K. (1)	+ -
McDonald, Jonathan Ryan. (1)	+ -
Miller, Warner A. (1)	+ -
Pace, Nicola (1)	+ -
Pillai, Ajay S. (1)	+ -
Qubbaj, Murad R. (1)	+ -
Steinwandt, Rainer (1)	+ -
Vaulin, Ruslan (1)	+ -
Yakunin, Konstantin. (1)	+ -

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