Contour gauges, canonical formalism and flux algebras

A broad class of contour gauges is shown to be determined by admissible con tractions of the geometrical region considered and a suitable equivalence c lass of curves is defined. In the special case of magnetostatics, the relev ant electromagnetic potentials are directly related to the ponderomotive fo rces. Schwinger's method of extracting a gauge invariant factor from the fe rmion propagator could, it is argued, lead to incorrect results. Dirac brac kets of both Maxwell and Yang-Mills theories are given for arbitrary admiss ible space-like paths. It is shown how to define a non-abelian flux and loc al charges which obey a local charge algebra. Fields associated with the ch arges differ from the electric fields of the theory by singular topological terms; to avoid this obstruction to the Gauss law it is necessary to exclu de a single, gauge fixing curve from the region considered. (C) 1999 Elsevi er Science B.V. All rights reserved.