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Articles 1 - 16 of 16
Full-Text Articles in Physics
What Is A Photon? Foundations Of Quantum Field Theory, Charles G. Torre
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.
A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Charles G. Torre
A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Charles G. Torre
Research Vignettes
No abstract provided.
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, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Spacetime Groups, Ian M. Anderson, Charles G. Torre
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,η), with g being a 4-dimensional Lie algebra and η 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 algorithmic solution to the …
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.
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 …
Variation Of The Linear Biconformal Action, James Thomas Wheeler
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
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
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
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
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.
Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
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
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
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
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
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.