Semiclassical Partition Functions for Gravity with Cosmic Strings

In this paper we describe an approach to construct semiclassical partition functions in gravity which are complete in the sense that they contain a complete description of the differentiable structures of the underlying 4-manifold. In addition, we find our construction naturally includes cosmic strings. We discuss some possible applications of the partition functions in the fields of both quantum gravity and topological string theoryComment: 17 pages, 2 figures, revisions of example

Topspin Networks in Loop Quantum Gravity

We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert space of cylindrical functions. We will also discuss the area and Hamiltonian operators, and show how they depend on the topology. This extends the idea of \u27background independence\u27 in loop quantum gravity to include topology as well as geometry. It is hoped this work will confirm the usefulness of the topspin network formalism and open up several new avenues for research into quantum gravity

Exotic Smoothness in Four Dimensions and Euclidean Quantum Gravity

In this paper we calculate the effect of the inclusion of exotic smooth structures on typical observables in Euclidean quantum gravity. We do this in the semiclassical regime for several gravitational free-field actions and find that the results are similar, independent of the particular action that is chosen. These are the first results of their kind in dimension four, which we extend to include one-loop contributions as well. We find these topological features can have physically significant results without the need for additional exotic physics

Application of Ampere\u27s Law to a Non-Infinite Wire and to a Moving Charge

In this work we demonstrate how to apply Ampere\u27s law to a non-infinite wire that is a part of a complete circuit with a steady current. We show that this can be done by considering the magnetic field from the whole circuit, without having to directly introduce the displacement current. This example can be used to isolate and clarify students\u27 confusion about the application of Ampere\u27s law to a short wire. The second part of this work focuses on the application of Ampere\u27s law to a non-relativistic moving charge. It exposes the students to the Dirac delta function in a physical example and guides them to finding the magnetic field of a moving charge in a reasonable way

Complementary Uses of the Magnetic Vector Potential for the Understanding and Teaching of Electromagnetics

This work reports on the uses of the magnetic vector potential A for understanding, visualizing and teaching electromagnetic phenomena. The teaching benefits of this work include examples of numerical modeling that facilitate understanding, and complementary visualization approaches. To facilitate discussion of A we first include a brief section looking at Φ in a system comprised of two hollow, positively charged spheres, demonstrating that the work required to bring the two spheres close together QΦ is equal to change in the total integrated electric field energy density. We then introduce a system comprised of a hollow, positively charged sphere interacting with two parallel, current-carrying wires, for which Awires is determined as a function of position. Two calculations of the field momentum of the system are compared and shown to be equal: the first is QAwires, the second is the integration over all space of the interaction momentum density ∈0E × B. We conclude by analyzing the trajectory of Q near the wires, establishing a visual connection between particle motion and the magnetic vector potentials sourced by the wires, including a discussion of relativistic implications

Metrics on End-Periodic Manifolds as Models for Dark Matter

In this paper we will detail an approach to generate metrics and matter models on end-periodic manifolds, which are used extensively in the study of the exotic smooth structures of R4. After an overview of the technique, we will present two specific examples, discuss the associated matter models by solving the Einstein equations, and determine the physical viability by examining the energy conditions. We compare the resulting model directly with existing models of matter distributions in extragalactic systems, to highlight the viability of utilizing exotic smooth structures to understand the existence and distribution of dark matter