Vortex, Defect, and Monopole Gauge Fields for Nambu-Goldstone Systems and their Phase Transitions or Theory of Fluctuating Multivalued Fields

Abstract

We survey the various uses of singular gauge fields which render an ideal description of ensembles of line- and surface-like excitations and explain phase transitions with the help of simple quadratic actions. Near a transition, the singular gauge fields can be transformed into ordinary complex fields called disorder fields which differ from Landau's order fields by developing a nonzero expectation value in the high-temperature phase.