Physics Commons^™

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 …

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. …

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.