Noncovariant Gauges in Canonical Formalism

By definition, gauge theories - among the cornerstones of fundamental theoretical physics - involve more degrees of freedom than required by the underlying physics. The unphysical degrees of freedom must be shown not to yield unwarranted effects at every step in the formalism where explicit Lorentz covariance is required. The present work presents, in a rigorous way, a consistent formulation for the handling of noncovariant gauges in the quantization and renormalization of gauge theories. Though the path integral method is very convenient for the proof of unitarity and renormalizability of gauge theories, the canonical formalism is eventually necessary to to expose the issues in a self-consistent way. These notes are written as an introduction to postgraduate students, lecturers and researchers in the field and assume prior knowledge of quantum field theory.