Hamiltonian constraint analysis of vector field theories with spontaneous Lorentz symmetry breaking

Recent investigations of various quantum-gravity theories have revealed a variety of possible mechanisms that lead to Lorentz violation. One of the more elegant of these mechanisms is known as Spontaneous Lorentz Symmetry Breaking (SLSB), where a vector or tensor field acquires a nonzero vacuum expectation value. As a consequence of this symmetry breaking, massless Nambu-Goldstone modes appear with properties similar to the photon in Electromagnetism. This thesis considers the most general class of vector field theories that exhibit spontaneous Lorentz violation-known as bumblebee models-and examines their candidacy as potential alternative explanations of E&M, offering the possibility that Einstein-Maxwell theory could emerge as a result of SLSB rather than of local U(1) gauge invariance. With this aim we employ Dirac's Hamiltonian Constraint Analysis procedure to examine the constraint structures and degrees of freedom inherent in three candidate bumblebee models, each with a different potential function, and compare these results to those of Electromagnetism. We find that none of these models share similar constraint structures to that of E&M, and that the number of degrees of freedom for each model exceeds that of Electromagnetism by at least two, pointing to the potential existence of massive modes or propagating ghost modes in the bumblebee theories.

Natural Theology: A Reevaluation of Christianity's Relationship to the Natural World

In this thesis I offer two separate arguments for the creation of an environmentally friendly Christian theology. These arguments, although interconnected, are roughly divided into the main chapters of the thesis. I will begin in Chapter Two by offering a negative argument against the assumption that the natural world is sinful. In their article Hauerwas and Berkman suggest that the suffering of animals is both an example of the sinful state of the environment and a justification for human separation from an unholy natural environment. In response to this view I will argue in the second chapter that the suffering of animals can be seen as part of God's intentions for our world. Suffering, in both the human and the larger world, is not evidence of a fundamental flaw in natural systems. Instead, the cycle of death and life found in the natural world can be profoundly spiritual.