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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.


What Is A Photon? Foundations Of Quantum Field Theory, Charles G. Torre Jun 2018

What Is A Photon? Foundations Of Quantum Field Theory, Charles G. Torre

All Physics Faculty Publications

This is a brief, informal, and relatively low-level course on the foundations of quantum field theory. The prerequisites are undergraduate courses in quantum mechanics and electromagnetism.


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.


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 ...


A Solution In Weyl Gravity With Planar Symmetry, James Thomas Wheeler May 2015

A Solution In Weyl Gravity With Planar Symmetry, James Thomas Wheeler

James Thomas Wheeler

We solve the Bach equation for Weyl gravity for the case of a static metric with planar symmetry. The solution is not conformal to the solution to the corresponding Einstein equation.


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 ...


The Spacetime Co-Torsion In Torsion-Free Biconformal Spaces, James Thomas Wheeler Feb 2015

The Spacetime Co-Torsion In Torsion-Free Biconformal Spaces, James Thomas Wheeler

James Thomas Wheeler

In preceding studies, [TR Gamma minus, TR Gamma plus] we showed that the solution for the connection of flat biconformal space also solves the curved space field equations for the torsion and co-torsion. We continued this investigation with an attempt to solve the full set of torsion and co-torsion field equations, with only the assumption of vanishing torsion and the known form of the metric. We successfully reduced the torsion equations to a single equation. Here, we reduce that equation to its essential degrees of freedom. We find that the spacetime co-torsion is entirely determined by the scale vector and ...


Variation Of The Weyl Action, James Thomas Wheeler Feb 2015

Variation Of The Weyl Action, James Thomas Wheeler

James Thomas Wheeler

We show how to vary the fourth order Weyl gravity action to derive the Bach equation.


Torsion Free Biconformal Spaces: Reducing The Torsion Field Equations, James Thomas Wheeler Jan 2015

Torsion Free Biconformal Spaces: Reducing The Torsion Field Equations, James Thomas Wheeler

James Thomas Wheeler

Our goal is to solve the full set of torsion and co-torsion field equations of Euclidean biconformal space, with only the assumption of vanishing torsion. Here we begin by resolving the involution constraints, symmetry conditions and torsion field equation into a single equation for further study.


Variation Of The Linear Biconformal Action, James Thomas Wheeler Jan 2015

Variation Of The Linear Biconformal Action, James Thomas Wheeler

All Physics Faculty Publications

We find the field equations of biconformal space in a basis adapted to Lagrangian submanifolds on which the restriction of the Killing metric is non-degenerate.


Studies In Torsion Free Biconformal Spaces. Case 2: \Gamma_{-} = 0, James Thomas Wheeler Jan 2015

Studies In Torsion Free Biconformal Spaces. Case 2: \Gamma_{-} = 0, James Thomas Wheeler

All Physics Faculty Publications

We show that the solutions for the symmetric part of the connection in homogeneous biconformal space also satisfy the more general field equations of curved biconformal spaces in the case when \gamma_{-} = 0.


Studies In Torsion Free Biconformal Spaces, James Thomas Wheeler Jan 2015

Studies In Torsion Free Biconformal Spaces, James Thomas Wheeler

All Physics Faculty Publications

We study whether the solutions for the symmetric part of the connection in homogeneous biconformal space also satisfy the more general field equation of curved biconformal spaces. We show that the six field equations for the torsion and co-torsion are satisfied by vanishing torsion together with the Lorentzian form of the metric when γ+ = 0.


Gauge Transformations Of The Biconformal Connection, James Thomas Wheeler Dec 2014

Gauge Transformations Of The Biconformal Connection, James Thomas Wheeler

All Physics Faculty Publications

We study the changes of the biconformal gauge fields under the local rotational and dilatational gauge transformations.


Rainich-Type Conditions For Perfect Fluid Spacetimes, Dionisios Krongos, Charles G. Torre Dec 2014

Rainich-Type Conditions For Perfect Fluid Spacetimes, Dionisios Krongos, Charles G. Torre

Research Vignettes

In this worksheet we describe and illustrate a relatively simple set of new Rainich-type conditions on an n-dimensional spacetime which are necessary and sufficient for it to define a perfect fluid solution of the Einstein field equations. Procedures are provided which implement these Rainich-type conditions and which reconstruct the perfect fluid from the metric. These results provide an example of the idea of geometrization of matter fields in general relativity, which is a purely geometrical characterization of matter fields via the Einstein field equations.


Gauge Theories Of General Relativity, James Thomas Wheeler Nov 2014

Gauge Theories Of General Relativity, James Thomas Wheeler

James Thomas Wheeler

General relativity can be seen as a gauge theory of the Lorentz, Poincaré, Weyl, de Sitter, or conformal groups. In most of these, there is little or no difference from the standard formulation in Riemannian geometry, but the higher symmetries — de Sitter and conformal — introduce new features and explain old ones. The potential presence of a cosmological constant, the spacetime metric, cosmological dust, symplectic structure, Kähler structure and even the existence of a timelike direction can all be seen to arise from the underlying group structure.


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 ...


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.