Diverse Topics in Theoretical and Mathematical Physics

Abstract

Part 1 Anomalies and fractional charge: non-canonical behaviour in canonical theories quantum mechanical symmetry breaking delta function potentials in two- and three-dimensional quantum mechanics update on anomalous theories effects of Dirac's negative energy sea on quantum numbers Fermion fractionization in physics the chiral anomaly. Part 2 Gauge theories and gravity: Yang-Mills vacuum as a bloch wave bifurcation and stability in Yang-Mills theory with sources Gauge theories in three dimensions (= at high temperature) planar gravity time travel? Gauge theories for gravity on a line. Part 3 Symmetry behavior: introducing scale symmetry hidden symmetry of the point magnetic monopole invariance, symmetry and periodicity in Gauge theories symmetry restoration at finite temperature mean field theory for non-equilibrium quantum fields. Part 4 Approaches to quantum theory following Dirac: canonical light-cone commutators and their applications invariant quantization, scale symmetry and Euclidean field theory (constrained) quantization without tears analysis on infinite-dimensional manifolds - Schrodinger representation for quantized fields. Part 5 Solitons, instantons and semi-classical quantum field theory: non-perturbative and topological methods in quantum field theory self-dual Chern-Simons solitions.