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.

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.

Enforcement in environmental law: an economic analysis of citizen suits

Previous to 1970, state and federal agencies held exclusive enforcement responsibilities over the violation of pollution control standards. However, recognizing that the government had neither the time nor resources to provide full enforcement, Congress created citizen suits. Citizen suits, first amended to the Clean Air Act in 1970, authorize citizens to act as private attorney generals and to sue polluters for violating the terms of their operating permits. Since that time, Congress has included citizen suits in 13 other federal statutes. The citizen suit phenomenon is sufficiently new that little is known about it. However, we do know that citizen suits have increased rapidly since the early 1980's. Between 1982 and 1986 the number of citizen suits jumped from 41 to 266. Obviously, they are becoming a widely used method of enforcing the environmental statutes. This paper will provide a detailed description, analysis and evaluation of citizen suits. It will begin with an introduction and will then move on to provide some historic and descriptive background on such issues as how citizen suit powers are delegated, what limitations are placed on the citizens, what parties are on each side of the suit, what citizens can enforce against, and the types of remedies available. The following section of the paper will provide an economic analysis of citizen suits. It will begin with a discussion of non-profit organizations, especially non-profit environmental organizations, detailing the economic factors which instigate their creation and activities. Three models will be developed to investigate the evolution and effects of citizen suits. The first model will provide an analysis of the demand for citizen suits from the point of view of a potential litigator showing how varying remedies, limitations and reimbursement procedures can effect both the level and types of activities undertaken. The second model shows how firm behavior could be expected to respond to citizen suits. Finally, a third model will look specifically at the issue of efficiency to determine whether the introduction of citizen enforcement leads to greater or lesser economic efficiency in pollution control. The database on which the analysis rests consists of 1205 cases compiled by the author. For the purposes of this project this list of citizen suit cases and their attributes were computerized and used to test a series of hypotheses derived from three original economic models. The database includes information regarding plaintiffs, defendants date notice and/or complaint was filed and statutes involved in the claim. The analysis focuses on six federal environmental statutes (Clean Water Act} Resource Conservation and Recovery Act, Comprehensive Environmental Response Compensation and Liability Act, Clean Air Act, Toxic Substances Control Act, and Safe Drinking Water Act) because the majority of citizen suits have occurred under these statutes.