## Doctoral Dissertations

#### Title

Topics in gauge theory

January 1998

#### Keywords

Physics, Elementary Particles and High Energy

Ph.D.

#### Abstract

This dissertation will present studies in three distinct areas of gauge theories. In Chern-Simons theories, the fate of the quantized Chern-Simons coupling constant upon renormalization of the theory is investigated. We find the Chern-Simons coupling constant remains quantized in the presence of residual non-abelian gauge symmetry. A two-flavor model of fermions is studied to determine the extent at which the vacuum condensate is locally proportional to the magnetic field. We find the proportionality is local in the limit of large flux. Using resolvent techniques, we find the exact effective action in a single pulsed electric background gauge field $E\sb1$(t) = Esech$\sp2$($t\over r$). We derive the zero and first order derivative expansion for this electric field and compare with our exact results. Dispersion relations between the real and imaginary parts of the exact effective action are derived. In a uniform semi-classical approximation, we find the exact effective action for a spatially homogeneous background electric field with general time dependence. ^

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