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Thesis (Ph. D.)--University of Texas at Austin, 2003. / Supervisor: Willy Fischler. Vita. Includes bibliographical references. Also available from UMI.

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No description available.

No description available.

No description available.

No description available.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Field theory is used to describe the material content of the universe throughout its entire history, and an oscillating cosmological model without a singularity is presented. In our theory, the “cosmological fluid” is described by a classical scalar field that undergoes a series of phase transitions over the lifetime of the universe. Each transition corresponds to a discontinuous change in the equation of state of the field. In general, for an FRW universe and a given equation of state, we show that the field potential V(Φ) may be derived from the solution of Piccati’s equation. The resulting expression for V(Φ) includes parameters whose values are determined from the boundary conditions. In our theory, we employ the standard cosmological model and the fundamental Planck quantities to provide these boundary conditions. We thereby determine the scalar field Lagrangian for the entire history of the universe. The resulting cosmological model is free of any singularities, and includes an early inflationary epoch. Inflation arises in our theory as a consequence of the initial conditions. The theory describes a universe that is very cold at its minimum radius, although it heats rapidly during the initial inflationary era. This increase in the temperature of the scalar field during inflation is a direct consequence of applying classical thermodynamics under the assumed conditions for the early universe, and does not depend on the fine-tuning of free parameters. Inflation continues until a maximum possible physical temperature (the Planck temperature) is attained, at which point a phase transition occurs and the standard model era begins. By relating the temperature of the scalar field in our theory to the radiation temperature in the standard model universe, it is possible to establish a thermodynamic constraint on a more complete theory of matter for the early universe. Although, in principle, inflation occurs for any equation of state where p < -(1/3)p, we find that the initial equation of state must be p ≈ -p if the later epochs of the universe are to resemble the standard model. In particular, we find that Ho = 33 - 44 km sec-1 Mpc-1 is the value of the Hubble parameter a t the current epoch that is least sensitive to the initial equation of state. / Graduate

Bibliography: pages 95-97. / A major obstacle to calculating Feynman diagrams in field theories, confined to a cavity, has always been the divergent loop diagrams. So far, only the quantum chromodynamic and electrodynamic self-energies of a ls1/2 quark, confined to a static spherical cavity, have been accurately calculated. These quantities are of immediate interest in the M.I.T. bag model. The existing methods to calculate loop diagrams are based on the multiple reflection scheme, in which the zero reflection term is separated out analytically, and evaluated separately. Thus far, there are some indications that this method is unsuitable for the quadratically divergent one loop vacuum polarization. In this thesis we firstly develop a set of Fourier transforms, appropriate to a discussion of renormalization in a cavity. Using these, we renormalize the cavity propagators to one loop for scalar, Dirac, and gauge fields. We then introduce a new computational method to subtract out the divergences, based on dimensional regularization. Using this method, we present results for various loop diagrams. The scalar φ⁴ theory is used as a pedagogical example. We then present the quark self-energy for several low lying cavity modes. Finally we tackle the long standing and hitherto unresolved question of the vacuum polarization. For this we give a detailed discussion of surface divergences, and present results for scalar quantum electrodynamics. We make a suggestion for the implementation of the running coupling constant in the cavity.