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.

Differential Habituation of Male Betta Splendens to Qualitatively Different Stimuli

Habituation is a learning mechanism that functions to decrease the amount of energy and attention focused on a certain stimuli. Male Siamese Fighting Fish, Betta splendens, are territorial animals that defend their territories using a number of aggressive displays. Male Bettas have previously shown the ability to habituate to the presence of a conspecific male when visually exposed to each other. Due to the costly nature of many of the male Betta’s displays, I hypothesized that male Bettas should differentially habituate to qualitatively different stimuli. I presented each of three groups of male Betta splendens with a different stimulus, each presenting a different level of interactivity. I predicted that the Bettas would be more likely to habituate to a less interactive stimulus than a more interactive one. No significant habituation was observed in any of the groups and no significant differences in latency to display or length of display between all three groups were observed. However, overall data trends suggest that habituation was indeed occurring and that the three different stimuli elicited different levels of display. The limited amount of visual exposure to the stimuli in this experiment might account for why results were insignificant.