Diverse Topics In Theoretical And Mathematical Physics: Lectures By Roman Jackiw

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.