Open Access. Powered by Scholars. Published by Universities.®
Elementary Particles and Fields and String Theory Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- 11/8th conjecture (1)
- Computer Algebra (1)
- Differential Geometry (1)
- Einstein Field Equations (1)
- Einstein equations (1)
-
- Gauge theory (1)
- General Relativity (1)
- Geometric analysis (1)
- High order methods (1)
- ISI journals (1)
- Isometry (1)
- Killing Vector (1)
- Lie Algebra (1)
- Low dimensional topology (1)
- Mathematical physics (1)
- Models of particle accelerators (1)
- Numerical partial differential equaitons (1)
- Overset grid methods (1)
- Perfect fluid (1)
- Rainich conditions (1)
- Rarita-Schwinger operator (1)
- Seiberg-Witten theory (1)
- Spin dynamics (1)
- Stochastic differential equations (1)
- Publication
- Publication Type
Articles 1 - 6 of 6
Full-Text Articles in Elementary Particles and Fields and String Theory
Finite Dimensional Approximation And Pin(2)-Equivariant Property For Rarita-Schwinger-Seiberg-Witten Equations, Minh Lam Nguyen
Finite Dimensional Approximation And Pin(2)-Equivariant Property For Rarita-Schwinger-Seiberg-Witten Equations, Minh Lam Nguyen
Graduate Theses and Dissertations
The Rarita-Schwinger operator Q was initially proposed in the 1941 paper by Rarita and Schwinger to study wave functions of particles of spin 3/2, and there is a vast amount of physics literature on its properties. Roughly speaking, 3/2−spinors are spinor-valued 1-forms that also happen to be in the kernel of the Clifford multiplication. Let X be a simply connected Riemannian spin 4−manifold. Associated to a fixed spin structure on X, we define a Seiberg-Witten-like system of non-linear PDEs using Q and the Hodge-Dirac operator d∗ + d+ after suitable gauge-fixing. The moduli space of solutions M contains (3/2-spinors, purely …
From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov
From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov
Mathematics & Statistics ETDs
In this work we concentrate on two separate topics which pose certain numerical challenges. The first topic is the spin dynamics of electrons in high-energy circular accelerators. We introduce a stochastic differential equation framework to study spin depolarization and spin equilibrium. This framework allows the mathematical study of known equations and new equations modelling the spin distribution of an electron bunch. A spin distribution is governed by a so-called Bloch equation, which is a linear Fokker-Planck type PDE, in general posed in six dimensions. We propose three approaches to approximate solutions, using analytical and modern numerical techniques. We also present …
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.
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.
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.
Local Fractional Fourier Series With Application To Wave Equation In Fractal Vibrating String, Yang Xiaojun
Local Fractional Fourier Series With Application To Wave Equation In Fractal Vibrating String, Yang Xiaojun
Xiao-Jun Yang
We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag- Leffler function.