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Articles 1 - 14 of 14
Full-Text Articles in Physics
Introduction To Classical Field Theory, Charles G. Torre
Introduction To Classical Field Theory, Charles G. Torre
All Complete Monographs
This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Spacetime Groups, Ian M. Anderson, Charles G. Torre
All Physics Faculty Publications
A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs, (g, n), with g being a 4-dimensional Lie algebra and n being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely …
Full Dyon Excitation Spectrum In Extended Levin-Wen Models, Yuting Hu, Alexandra Tebbs, Yong-Shi Wu
Full Dyon Excitation Spectrum In Extended Levin-Wen Models, Yuting Hu, Alexandra Tebbs, Yong-Shi Wu
Mathematics and Statistics Faculty Publications
In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two-dimensional topological phases, it is relatively easy to describe only single-fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological phases, an extension of the LW models is proposed in this paper. We first enlarge the Hilbert space with adding a tail on one of the edges of each trivalent vertex to describe the internal charge degrees of freedom at the vertex. Then, we study the full dyon spectrum of the extended LW models, including …
Foundations Of Wave Phenomena, Charles G. Torre
Foundations Of Wave Phenomena, Charles G. Torre
Charles G. Torre
This is an undergraduate text on the mathematical foundations of wave phenomena. Version 8.2.
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Charles G. Torre
Rainich-type conditions giving a spacetime “geometrization” of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and electromagnetic fields. Necessary and sufficient conditions on a spacetime metric for it to be part of a perfect fluid solution of the Einstein equations are given. Formulas for constructing the fluid from the metric are obtained. All fluid results hold for any spacetime dimension. Geometric conditions on a metric which are necessary and sufficient for it to define a solution of the Einstein-scalar field equations and formulas for constructing the scalar field from …
Explicit Construction Of First Integrals For The Toda Flow On A Classical Simple Lie Algebra, Patrick Seegmiller
Explicit Construction Of First Integrals For The Toda Flow On A Classical Simple Lie Algebra, Patrick Seegmiller
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
The Toda flow is a generalization of a dynamical system describing the interaction of particles in a one-dimensional crystal. The concepts and energy and conservation are prominent in the study of dynamical systems, and quantities which remain the same over the evolution of a system provide valuable insights into the system’s behavior. In the realm of mathematics these quantities are called first integrals, or integrals of motion. This paper provides a background for study of the Toda flow, a verification of its integrability, and programming code for finding these quantities which remain unchanged over the evolution of the system.
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Presentations and Publications
Rainich-type conditions giving a spacetime “geometrization” of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and elec- tromagnetic fields. Necessary and sufficient conditions on a spacetime metric for it to be part of a perfect fluid solution of the Einstein equa- tions are given. Formulas for constructing the fluid from the metric are obtained. All fluid results hold for any spacetime dimension. Ge- ometric conditions on a metric which are necessary and sufficient for it to define a solution of the Einstein-scalar field equations and for- mulas for constructing …
Perihelion Precession In General Relativity, Charles G. Torre
Perihelion Precession In General Relativity, Charles G. Torre
Charles G. Torre
This is a Maple worksheet providing a relatively quick and informal sketch of a demonstration that general relativistic corrections to the bound Kepler orbits introduce a perihelion precession. Any decent textbook will derive this result. My analysis aligns with that found in the old text "Introduction to General Relativity", by Adler, Bazin and Schiffer. The plan of the analysis is as follows. * Model the planetary orbits as geodesics in the (exterior) Schwarzschild spacetime. * Compute the geodesic equations. * Simplify them using symmetries and first integrals. * Isolate the differential equation expressing the radial coordinate as a function of …
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
Charles G. Torre
We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from …
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
Presentations and Publications
We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from …
Particle Dynamics And Resistivity Characteristics In Bifurcated Current Sheets, Tushar Andriyas
Particle Dynamics And Resistivity Characteristics In Bifurcated Current Sheets, Tushar Andriyas
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Charged particle chaos and its collective effects in different magnetic geometries are investigated in a sequence of various numerical experiments. The fields generated by the particles as a result of interaction with the background electric and magnetic fields is not accounted for in the simulation. An X-line is first used to describe the geometry of the magnetotail prior to magnetic reconnection and a study of the behavior of charged particles is done from a microscopic viewpoint. Another important geometry in the magnetotail prior to substorm onset is Bifurcated Current Sheet. The same analysis is done for this configuration. The existence …
Estimation And Testing For Spatially Indexed Curves With Application To Ionospheric And Magnetic Field Trends, Oleksandr Gromenko, Piotr Kokoszka, Lie Zhu, Jan Josef Sojka
Estimation And Testing For Spatially Indexed Curves With Application To Ionospheric And Magnetic Field Trends, Oleksandr Gromenko, Piotr Kokoszka, Lie Zhu, Jan Josef Sojka
All Physics Faculty Publications
We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves X(sk;t), t∈[0, T], observed at spatial locations s1,s2, . . . ,sN. We propose several methods, and evaluate them by means of a simulation study. Next, we develop a significance test for the correlation of two such functional spatial fields. After validating the finite sample performance of this test by means of a simulation study, we apply it to determine if there is correlation between long-term trends in the so-called critical ionospheric frequency …
Classical Foundations For A Quantum Theory Of Time In A Two-Dimensional Spacetime, Nathan Thomas Carruth
Classical Foundations For A Quantum Theory Of Time In A Two-Dimensional Spacetime, Nathan Thomas Carruth
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
We consider the set of all spacelike embeddings of the circle S1 into a spacetime R1 × S1 with a metric globally conformal to the Minkowski metric. We identify this set and the group of conformal isometries of this spacetime as quotients of semidirect products involving diffeomorphism groups and give a transitive action of the conformal group on the set of spacelike embeddings. We provide results showing that the group of conformal isometries is a topological group and that its action on the set of spacelike embeddings is continuous. Finally, we point out some directions for future research.
Asymptotic Conservation Laws In Classical Field Theory, Ian M. Anderson, Charles G. Torre
Asymptotic Conservation Laws In Classical Field Theory, Ian M. Anderson, Charles G. Torre
Mathematics and Statistics Faculty Publications
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity.