Elementary Particles and Fields and String Theory Commons^™

Renormalized Stress-Energy Tensor For Scalar Fields In Hartle-Hawking, Boulware, And Unruh States In The Reissner-Nordström Spacetime, Julio Arrechea, Cormac Breen, Adrian Ottewill, Peter Taylor

Articles

In this paper, we consider a quantum scalar field propagating on the Reissner-Nordström black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed “extended coordinate” prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a …

Deep Virtual Pion Pair Production, Dilini Lakshani Bulumulla

Physics Theses & Dissertations

This experiment investigates the deep virtual production of both σ− and ρ− mesons, with a particular focus on the microscopic structure of the σ mesons. While the ρ meson is an ordinary qq¯ pair, the σ meson is composed of not only the typical qq¯ pair, making it a topic of controversy for nearly six decades. Although the existence of the σ− meson is now well established, its microscopic structure remains poorly understood. The primary objective of this thesis is to contribute to the understanding of the σ meson by analyzing its deep virtual production. The main focus of this …

Modified Geometries, Clifford Algebras And Graphs: Their Impact On Discreteness, Locality And Symmetr, Roman Sverdlov

Mathematics & Statistics ETDs

In this dissertation I will explore the question whether various entities commonly used in quantum field theory can be “constructed". In particular, can spacetime be “constructed" out of building blocks, and can Berezin integral be “constructed" in terms of Riemann integrals.

As far as “constructing" spacetime out of building blocks, it has been attempted by multiple scientific communities and various models were proposed. But the common downfall is they break the principles of relativity. I will explore the ways of doing so in such a way that principles of relativity are respected. One of my approaches is to replace points …

A Mode-Sum Prescription For The Renormalized Stress Energy Tensor On Black Hole Spacetimes, Peter Taylor, Cormac Breen, Adrian Ottewill

Articles

In this paper, we describe an extremely efficient method for computing the renormalized stress-energy tensor of a quantum scalar field in spherically symmetric black hole spacetimes. The method applies to a scalar field with arbitrary field parameters. We demonstrate the utility of the method by computing the renormalized stress-energy tensor for a scalar field in the Schwarzschild black hole spacetime, applying our results to discuss the null energy condition and the semiclassical backreaction.

Classification Of Pixel Tracks To Improve Track Reconstruction From Proton-Proton Collisions, Kebur Fantahun, Jobin Joseph, Halle Purdom, Nibhrat Lohia

SMU Data Science Review

In this paper, machine learning techniques are used to reconstruct particle collision pathways. CERN (Conseil européen pour la recherche nucléaire) uses a massive underground particle collider, called the Large Hadron Collider or LHC, to produce particle collisions at extremely high speeds. There are several layers of detectors in the collider that track the pathways of particles as they collide. The data produced from collisions contains an extraneous amount of background noise, i.e., decays from known particle collisions produce fake signal. Particularly, in the first layer of the detector, the pixel tracker, there is an overwhelming amount of background noise that …

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.

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 …

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

Several Problems In Nonlinear Schrödinger Equations, Tim Van Hoose

Masters Theses

“We study several different problems related to nonlinear Schrödinger equations….

We prove several new results for the first equation: a modified scattering result for both an averaged version of the equation and the full equation, as well as a set of Strichartz estimates and a blowup result for the 3d cubic problem.

We also present an exposition of the classical work of Bourgain on invariant measures for the second equation in the mass-subcritical regime”--Abstract, page iv.

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 …

A Short Remark On Vortex As Fluid Particle From Neutrosophic Logic Perspective, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In a previous paper in this journal (IJNS), it is mentioned about a possible approach to re-describe QED without renormalization route. As it is known that in literature, there are some attempts to reconcile vortex-based fluid dynamics and particle dynamics. Some attempts are not quite as fruitful as others. As a follow up to previous paper, the present paper will discuss two theorems for developing unification theories, and then point out some new proposals including by Simula (2020) on how to derive Maxwell equations in superfluid dynamics setting; this could be a new alternative approach towards “fluidicle” or “vorticle” model …

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 …

Power Corrections To Tmd Factorization For Z-Boson Production, I. Balitsky, A. Tatasov

Physics Faculty Publications

A typical factorization formula for production of a particle with a small transverse momentum in hadron-hadron collisions is given by a convolution of two TMD parton densities with cross section of production of the final particle by the two partons. For practical applications at a given transverse momentum, though, one should estimate at what momenta the power corrections to the TMD factorization formula become essential. In this paper we calculate the first power corrections to TMD factorization formula for Z-boson production and Drell-Yan process in high-energy hadron-hadron collisions. At the leading order in N_c power corrections are expressed in …

Numerical Simulation For A Rising Bubble Interacting With A Solid Wall: Impact, Bounce, And Thin Film Dynamics, Changjuan Zhang, Jie Li, Li-Shi Luo, Tiezheng Qian

Mathematics & Statistics Faculty Publications

Using an arbitrary Lagrangian-Eulerian method on an adaptive moving unstructured mesh, we carry out numerical simulations for a rising bubble interacting with a solid wall. Driven by the buoyancy force, the axisymmetric bubble rises in a viscous liquid toward a horizontal wall, with impact on and possible bounce from the wall. First, our simulation is quantitatively validated through a detailed comparison between numerical results and experimental data. We then investigate the bubble dynamics which exhibits four different behaviors depending on the competition among the inertial, viscous, gravitational, and capillary forces. A phase diagram for bubble dynamics has been produced using …

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.

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.