Elementary Particles and Fields and String Theory Commons^™

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

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.

Installation instructions

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

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.

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

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 …

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

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... 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.

Exact Topological Density In The Lattice Skyrme Model, Alec Schramm, Benjamin Svetitsky

Alec J Schramm

We propose using the Skyrme model on a lattice as an effective field theory of meson–baryon interactions. To this end we construct a local topological density that involves the volumes of tetrahedra in the target space S3 and we make use of Coxeter’s formula for the Schla¨fli function to implement it. We calculate the mean-square radius of a skyrmion in the three-dimensional Skyrme model, and find some surprises.

Topology And Metastability In The Lattice Skyrme Model, Alec Schramm, Benjamin Svetitsky

Alec J Schramm

We offer the Skyrme model on a lattice as an effective field theory—fully quantized—of baryon-meson interactions at temperatures below the chiral phase transition. We define a local topological density that involves the volumes of tetrahedra in the target space S3 and we make use of Coxeter’s formula for the Schläfli function to implement it. This permits us to calculate the mean-square radius of a Skyrmion in the three-dimensional lattice Skyrme model, which may be viewed as a Ginzburg-Landau effective theory for the full quantum theory at finite temperature. We find that, contrary to expectations, the Skyrmion shrinks as quantum and …

Glueball Production In Peripheral Heavy-Ion Collisions, Alec Schramm

Alec J Schramm

The method of equivalent quanta is applied both to photon-photon and, by analogy, to double pomeron exchange in heavy-ion collisions. This Weizsäcker-Williams approach is used to calculate production cross sections for the glueball candidate fJ(1710) meson via photon-photon and pomeron-pomeron fusion in peripheral heavy-ion collisions at both RHIC and LHC energies. The impact parameter dependence for total and elastic cross sections is presented, and compared with results for proton-proton collisions.

Production Of Η Mesons In Double Pomeron Exchange, Alec Schramm, Daniel Reeves

Alec J Schramm

We estimate the production cross section for ηc and ηb mesons via Pomeron-Pomeron fusion in peripheral heavy-ion collisions. Total and elastic PP cross sections are calculated in an equivalent Pomeron approximation.

Η Production In Peripheral Heavy-Ion Collisions, Alec Schramm, Daniel Reeves

Alec J Schramm

We estimate the impact parameter dependence of the production cross section for ηc and ηb mesons in peripheral heavy-ion collisions. Total and elastic γγ cross sections are calculated in an equivalent photon approximation.

Pion Fusion In Peripheral Pp Collisions, Alec Schramm, Burndt Muller

Alec J Schramm

We estimate the cross section for quasielastic double pion exchange in high energy proton-proton collisions. Total and elastic ππ cross sections are calculated in an equivalent pion approximation, with pion-baryon vertices taken from chiral perturbation theory.

Ab Initio Approach To The Deuteron In The Skyrme-Witten Model, Alec Schramm

Alec J Schramm

No abstract provided.