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.

Vector Theory of Spontaneous Lorentz Violation

Classical electromagnetism predicts two massless propagating modes, which are known as the two polarizations of the photon. On the other hand, if the Lorentz symmetry of classical electromagnetism is spontaneously broken, the new theory will still have two massless Nambu-Goldstone modes resembling the photon. If the Lorentz symmetry is broken by a bumblebee potential that allows for excitations out of the minimum, then massive modes arise. Furthermore, in curved spacetime, such massive modes will be created through a process other than the usual Higgs mechanism because of the dependence of the bumblebee potential on both the vector field and the metric tensor. Also, it is found that these massive modes do not propagate due to the extra constraints.

Photochemical Generation and Intramolecular Chemistry of β-Alkoxycarbenes

The photolytic phenanthrene-based precursors for both β-methoxycarbene and β-ethoxycarbene were synthesized with and without a deuterium label attached to the a carbon. The incorporation of this deuterium label allowed distinction between a 1, 2-H shift and a 1, 2-O shift pathway to the respective alkyl vinyl ether, without the influence of a primary kinetic isotope effect. Photolyses of these precursors gave rearrangement products of the expected β-alkoxycarbenes. In the case of β-methoxycarbene, no methyl vinyl ether was observed due to its volatility. However, the appearance of aldehyde peaks in the NMR spectra, from an apparent further rearrangement to acetaldehyde through an enol intermediate, indicated that a 1,2-H shift had occurred. Ethyl vinyl ether was isolated following the photolysis of the β-ethoxycarbene precursor. Quantification of the two pathways showed less than 2% undergoing an ethoxy shift to the ethyl vinyl ether. Yield experiments on this photolysis demonstrated a maximum yield of β-ethoxycarbene as 43%, though this decreased as the experiment continued. Computational work on the β-ethoxycarbene system indicates that the triplet scate is more stable than the singlet. In addition, the activation energy to the 1.2-H shift pathway is remarkably low and is clearly consistent with the observed overwhelming preference for this pathway in the experiment.