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Full-Text Articles in Physics

Introduction To Classical Field Theory, Charles G. Torre Aug 2019

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.


Full Dyon Excitation Spectrum In Extended Levin-Wen Models, Yuting Hu, Nathan Geer, Yong-Shi Wu May 2018

Full Dyon Excitation Spectrum In Extended Levin-Wen Models, Yuting Hu, Nathan Geer, 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 ...


Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre Dec 2017

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 Dec 2016

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 Jan 2016

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.

Installation instructions


Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos Jul 2015

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 May 2015

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 Mar 2015

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 Apr 2014

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 Feb 2014

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 ...


Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre Oct 2013

Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre

Research Vignettes

In this second of two worksheets I continue describing local Rainich-type 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 Einstein-Maxwell 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 Jul 2013

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 May 2013

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 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 ...


How To Find Killing Vectors, Charles G. Torre Mar 2013

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 Einstein-Maxwell Equations, Charles G. Torre Jul 2012

A Homogeneous Solution Of The Einstein-Maxwell 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 Einstein-Maxwell equations.

PDF and Maple worksheets can be downloaded from the links below.


How To Create A Lie Algebra, Ian M. Anderson Jul 2012

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 Jun 2012

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 long-term trends in the so-called critical ionospheric ...


Classical Foundations For A Quantum Theory Of Time In A Two-Dimensional Spacetime, Nathan Thomas Carruth May 2010

Classical Foundations For A Quantum Theory Of Time In A Two-Dimensional 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 Jan 1996

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.