Open Access. Powered by Scholars. Published by Universities.^{®}
 Keyword

 General Relativity (6)
 Rainich Conditions (4)
 Presentation (3)
 Einstein Field Equations (3)
 EinsteinMaxwell Equations (3)

 Electrovacuum (3)
 EinsteinMaxwell equations (2)
 Classical field theory (2)
 Einsteinscalar field equations (2)
 Einsteinfluid equations (2)
 Covers of diffeomorphism and infinitedimensional topological groups (1)
 Geodesics (1)
 Computer Algebra (1)
 Electromagnetic field (1)
 Algebra (1)
 Infinitedimensional topological groups (1)
 Dirac field (1)
 Hamiltonian (1)
 Gravitational field (1)
 Functional data analysis; Ionospheric trends; Spatial statistics (1)
 Flow (1)
 Electric and Magnetic Fields (1)
 Fourier Analysis (1)
 Asymptotic conservation laws (1)
 Grouptheoretic quantization (1)
 Diffeomorphism groups (1)
 DifferentialGeometry (1)
 Conservation Laws (1)
 Differential Geometry (1)
 Geometric topology (1)
 Publication Year
 Publication
 Publication Type
Articles 1  19 of 19
FullText 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: KleinGordon field, electromagnetic field, scalar electrodynamics, Dirac field, YangMills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.
Full Dyon Excitation Spectrum In Extended LevinWen Models, Yuting Hu, Nathan Geer, YongShi Wu
Full Dyon Excitation Spectrum In Extended LevinWen Models, Yuting Hu, Nathan Geer, YongShi Wu
Mathematics and Statistics Faculty Publications
In LevinWen (LW) models, a wide class of exactly solvable discrete models, for twodimensional topological phases, it is relatively easy to describe only singlefluxon excitations, but not the charge and dyonic as well as manyfluxon 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 ...
Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre
Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre
Tutorials on... in 1 hour or less
This is a Maple worksheet providing an introduction to the USU Library of Solutions to the Einstein Field Equations. The library is part of the DifferentialGeometry software project and is a collection of symbolic data and metadata describing solutions to the Einstein equations.
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.
The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre
The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre
Downloads
This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple. It has been tested on Maple versions 17, 18, 2015.
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
Rainichtype 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 Einsteinscalar 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
The Toda flow is a Hamiltonian system which evolves on the dual of the Borel subalgebra of a complex Lie algebra g. The dual of the Borel subalgebra can be identified with an affine subspace of its negative plus the element given by the sum of the simple root vectors in g. The system has been proven completely integrable in the Liouville sense on a generic coadjoint orbit for the Borel subgroup. This paper gives a verification of integrability of the Toda flow on classical simple Lie algebras and describes a method for the construction of a complete collection of ...
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
Rainichtype 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 Einsteinscalar 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 orbital angle  the "equation ...
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 EinsteinMaxwell 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 nonnull electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from ...
RainichType Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
RainichType Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
Research Vignettes
In this second of two worksheets I continue describing local Rainichtype conditions which are necessary and sufficient for the metric to define a null electrovacuum. In other words, these conditions, which I will call the null electrovacuum conditions, guarantee the existence of a null electromagnetic field such that the metric and electromagnetic field satisfy the EinsteinMaxwell equations. When it exists, the electromagnetic field is easily constructed from the metric. In this worksheet I consider the null electrovacuum conditions which apply when a certain null geodesic congruence determined by the metric is twisting. I shall illustrate the these conditions using a ...
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 EinsteinMaxwell 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 nonnull 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
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 Xline 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 ...
How To Find Killing Vectors, Charles G. Torre
How To Find Killing Vectors, Charles G. Torre
How to... in 10 minutes or less
We show how to compute the Lie algebra of Killing vector fields of a metric in Maple using the commands KillingVectors and LieAlgebraData. A Maple worksheet and a PDF version can be found below.
A Homogeneous Solution Of The EinsteinMaxwell Equations, Charles G. Torre
A Homogeneous Solution Of The EinsteinMaxwell Equations, Charles G. Torre
Research Vignettes
We exhibit and analyze a homogeneous spacetime whose source is a pure radiation electromagnetic field [1]. It was previously believed that this spacetime is the sole example of a homogeneous pure radiation solution of the Einstein equations which admits no electromagnetic field (see [2] and references therein). Here we correct this error in the literature by explicitly displaying the electromagnetic source. This result implies that all homogeneous pure radiation spacetimes satisfy the EinsteinMaxwell equations.
PDF and Maple worksheets can be downloaded from the links below.
How To Create A Lie Algebra, Ian M. Anderson
How To Create A Lie Algebra, Ian M. Anderson
How to... in 10 minutes or less
We show how to create a Lie algebra in Maple using three of the most common approaches: matrices, vector fields and structure equations. PDF and Maple worksheets can be downloaded from the links below.
Estimation And Testing For Spatially Indexed Curves With Application To Ionospheric And Magnetic Field Trends, Oleksandr Gromenko, Piotr Kokoszka, Lie Zhu, Jan J. Sojka
Estimation And Testing For Spatially Indexed Curves With Application To Ionospheric And Magnetic Field Trends, Oleksandr Gromenko, Piotr Kokoszka, Lie Zhu, Jan J. 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 longterm trends in the socalled critical ionospheric ...
Classical Foundations For A Quantum Theory Of Time In A TwoDimensional Spacetime, Nathan Thomas Carruth
Classical Foundations For A Quantum Theory Of Time In A TwoDimensional Spacetime, Nathan Thomas Carruth
All Graduate Theses and Dissertations
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 ArnowittDeserMisner energy in general relativity.