Digital Commons Network^™

Yang-Mills Sources In Biconformal Double Field Theory, Davis W. Muhwezi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

There is a robust and unifying approach to unraveling the roiling mysteries of the universe. Our most compelling accounts of physical reality at present rest on symmetry arguments that are conspicuously geometrical!

105 years ago, Albert Einstein derived gravity from Riemannian geometry. In the general theory of relativity, the world of our experience is a pseudo-Riemannian manifold whose curvature represents the gravitational field. Encoded in the Einstein field equation is how matter sources (energy-momentum tensor) couple to gravity (spacetime curvature). Schematically, the Einstein equation exhibits a more general structure:

Curvature of Spacetime = Material Sources

On one side of the …

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 …

Instanton Counting, Matrix Models, And Characters, Spencer Tamagni

Honors Undergraduate Theses

In this thesis we study symmetries of quantum field theory visible only at the non-perturbative level, which arise from large deformations of the integration contour in the path integral. We exposit the recently-developed theory of qq-characters that organizes such symmetries in the case of N = 2 supersymmetric gauge theories in four dimensions. We sketch the physical origin of such observables from intersecting branes in string theory, and the mathematical origin as certain
equivariant integrals over Nakajima quiver varieties. We explain some of the main applications, including the derivation of Seiberg-Witten geometry for quiver gauge theories and the relations to …

Smooth Loops And Loop Bundles, Sergey Grigorian

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A loop is a rather general algebraic structure that has an identity element and division, but is not necessarily associative. Smooth loops are a direct generalization of Lie groups. A key example of a non-Lie smooth loop is the loop of unit octonions. In this paper, we study properties of smooth loops and their associated tangent algebras, including a loop analog of the Maurer-Cartan equation. Then, given a manifold, we introduce a loop bundle as an associated bundle to a particular principal bundle. Given a connection on the principal bundle, we define the torsion of a loop bundle structure and …

Field Theories From Physical Requirements: Noether's First Theorem, Energy-Momentum Tensors And The Question Of Uniqueness, Mark Robert Baker

Electronic Thesis and Dissertation Repository

An axiomatic approach to physics is proposed for obtaining classical gauge theories from a common set of physical requirements based on standard features of special relativistic field theories such as gauge invariance, conformal invariance and being in four dimensions. This approach involves the use of Noether's first theorem to directly obtain a unique, complete set of equations from the symmetries of the action. However, implementation of this procedure is obstructed by issues of ambiguity and non-uniqueness associated with the conserved tensors in the majority of special relativistic field theories. In the introductory chapter, we outline the three major problems which …

Particle Dynamics In Anti-De Sitter Space By Eih Method, Jiusi Lei

Dissertations, Theses, and Capstone Projects

Following the work of Einstein, Infeld and Hoffmann, we show that particle dynamics in Anti-de Sitter spacetime can be built up by regarding singularities in spacetime manifold as the source of particles.

Since gauge fields play a foundational role in the action, the singularities are chosen to be point-like instantons. Their winding number, defined by an integration on the spheres surrounding those singularities, will turn out to be related to their masses. And their action, derived from the Chern-Simons forms, will be a co-adjoint orbit action, with group element g ∈ SO(4, 2) describing the collective coordinates of the particle. …

General Relativity As A Biconformal Gauge Theory, James Thomas Wheeler

All Physics Faculty Publications

We consider the conformal group of a space of dim n=p+q, with SO(p,q) metric. The quotient of this group by its homogeneous Weyl subgroup gives a principal fiber bundle with 2n-dim base manifold and Weyl fibers. The Cartan generalization to a curved 2n-dim geometry admits an action functional linear in the curvatures. Because symmetry is maintained between the translations and the special conformal transformations in the construction, these spaces are called biconformal; this same symmetry gives biconformal spaces overlapping structures with double field theories, including manifest T-duality. We establish that biconformal geometry is …

An Overview Of Computational Mathematical Physics: A Deep Dive On Gauge Theories, Andre Simoneau

CMC Senior Theses

Over the course of a college mathematics degree, students are inevitably exposed to elementary physics. The derivation of the equations of motion are the classic examples of applications of derivatives and integrals. These equations of motion are easy to understand, however they can be expressed in other ways that students aren't often exposed to. Using the Lagrangian and the Hamiltonian, we can capture the same governing dynamics of Newtonian mechanics with equations that emphasize physical quantities other than position, velocity, and acceleration like Newton's equations do. Building o of these alternate interpretations of mechanics and understanding gauge transformations, we begin …

Selected Topics In Quantization And Renormalization Of Gauge Fields, Chenguang Zhao

Electronic Thesis and Dissertation Repository

My thesis covers several topics in the quantization and renormalization of gauge fields, ranging from the application of Dirac constraint procedure on the light front, to the manipulation of Faddeev-Popov method to enable use of the transverse-traceless gauge in first order gravity. Last, I study renormalization group ambiguities and carry out a new characterization method for models with one, two and five couplings.

In chapter 2 we apply the Dirac constraint procedure to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting …

Photoproduction And Radiative Decay Of Ηt Meson In Clas At Jlab, Georgie Mbianda Njencheu

Physics Theses & Dissertations

In this work the η/ meson photoproduction cross sections as well as the distribution of the di-pion invariant mass, m(π+π−), in the radiative decay mode η/ → π+π−γ have been measured using the CLAS detector at the Thomas Jefferson National Accelerator Facility using tagged incident photons in the center-of-mass energy range 1.96 GeV - 2.72 GeV. The measurements are performed on a liquid hydrogen target in the reaction γp → pη/(η/ → π+π−γ). The analysis is based on the …

Two Dimensional Lattice Gauge Theory With And Without Fermion Content, Dibakar Sigdel

FIU Electronic Theses and Dissertations

Quantum Chromo Dynamics (QCD) is a relativistic field theory of a non-abelian gauge field coupled to several flavors of fermions. Two dimensional (one space and one time) QCD serves as an interesting toy model that shares several features with the four dimensional physically relevant theory. The main aim of the research is to study two dimensional QCD using the lattice regularization.

Two dimensional QCD without any fermion content is solved analytically using lattice regularization. Explicit expressions for the expectation values of Wilson loops and the correlation of two Polyakov loops oriented in two different directions are obtained. Physics of the …

Some 2-Categorical Aspects In Physics, Arthur Parzygnat

Dissertations, Theses, and Capstone Projects

2-categories provide a useful transition point between ordinary category theory and infinity-category theory where one can perform concrete computations for applications in physics and at the same time provide rigorous formalism for mathematical structures appearing in physics. We survey three such broad instances. First, we describe two-dimensional algebra as a means of constructing non-abelian parallel transport along surfaces which can be used to describe strings charged under non-abelian gauge groups in string theory. Second, we formalize the notion of convex and cone categories, provide a preliminary categorical definition of entropy, and exhibit several examples. Thirdly, we provide a universal description …

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 …

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.

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

All Physics Faculty Publications

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

Weyl Gravity As General Relativity, James Thomas Wheeler

James Thomas Wheeler

When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This result differs strongly from the usual fourth-order formulation of Weyl gravity.

On Globally Non-Trivial Almost-Commutative Manifolds, Jord Boeijink, Koen Van Den Dungen

Faculty of Engineering and Information Sciences - Papers: Part A

Within the framework of Connes’ noncommutative geometry, we define and study globally non-trivial (or topologically non-trivial) almost-commutative manifolds. In particular, we focus on those almost-commutative manifolds that lead to a description of a (classical) gauge theory on the underlying base manifold. Such an almost-commutative manifold is described in terms of a “principal module,” which we build from a principal fibre bundle and a finite spectral triple. We also define the purely algebraic notion of “gauge modules,” and show that this yields a proper subclass of the principal modules. We describe how a principal module leads to the description of a …

A Gauge Theoretic Treatment Of Rovibrational Motion In Diatoms, Gregory Colarch

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Born-Oppenheimer approximation has long been the standard approach to solving the Schrödinger equation for diatomic molecules. In it, nuclear and electronic motions are separated into "slow" and "fast" degrees of freedom and couplings between the two are ignored. The neglect of non-adiabatic couplings leads to an incomplete description of diatomic motion, and in a more refined approach, non-adiabatic couplings are uncoupled by transforming the angular momentum of the molecule and electrons into the body-fixed frame.

In this thesis we examine a "modern" form of the Born-Oppenheimer approximation by exploiting a gauge theoretic approach in a description of molecular motion. …

Stability, Creation And Annihilation Of Charges In Gauge Theories, Anton Ilderton, Martin Lavelle, David Mcmullan

School of Engineering, Computing and Mathematics

We show how to construct physical, minimal energy states for systems of static and moving charges. These states are manifestly gauge invariant. For charge–anticharge systems we also construct states in which the gauge fields are restricted to a finite volume around the location of the matter fields. Although this is an excited state, it is not singular, unlike all previous finite volume descriptions. We use our states to model the processes of pair creation and annihilation.

Determing The Properties Of Dense Matter: Superconductivity, Bulk Viscosity, And Light Reflection In Compact Stars, Gerald Good

All Theses and Dissertations (ETDs)

In this dissertation, we investigate the properties of matter, denser than nuclei, that exists inside compact stars. First, we examine a mixed superfluid/superconductor system, which likely occurs in neutron star cores. We derive an effective theory of Cooper pair quasiparticles from a microscopic theory of nucleons, and calculate the coupling strengths between quasiparticles. We then calculate the structure of magnetic flux tubes, taking into consideration interactions between neutron and proton Cooper pairs. We find that interactions between the condensates can lead to interesting phenomena and new phases at the border between type-I and type-II behavior. Next, we examine the response …

Gauging Newton’S Law, James Thomas Wheeler

All Physics Faculty Publications

We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of dynamics with measurement. Applying this principle to Newton's law with the simplest measurement theory leads to Lagrangian mechanics, while use of conformal measurement theory leads to Hamiltonian mechanics.PACS Nos.: 45.20.Jj, 11.25.Hf, 45.10.–b [ABSTRACT FROM AUTHOR]

Biconformal Matter Actions, A. Wehner, James Thomas Wheeler

All Physics Faculty Publications

We extend 2n-dim biconformal gauge theory by including Lorentz-scalar matter fields of arbitrary conformal weight. We show that for a massless scalar field of conformal weight zero in a torsion-free biconformal geometry, the solution is determined by the Einstein equation on an n-dim submanifold, with the stress-energy tensor of the scalar field as source. The matter field satisfies the n-dim Klein-Gordon equation.

Why Quantum Mechanics Is Complex, James Thomas Wheeler

All Physics Faculty Publications

The zero-signature Killing metric of a new, real-valued, 8-dimensional gauging of the conformal group accounts for the complex character of quantum mechanics. The new gauge theory gives manifolds which generalize curved, relativistic phase space. The difference in signature between the usual momentum space metric and the Killing metric of the new geometry gives rise to an imaginary proportionality constant connecting the momentumlike variables of the two spaces. Path integral quantization becomes an average over dilation factors, with the integral of the Weyl vector taking the role of the action. Minimal U(1) electromagnetic coupling is predicted.