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arXiv · hep-th/9906026

Contour gauges, canonical formalism and flux algebras

L. Lukaszuk·E. Leader·A. Johansen
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Abstract

A broad class of contour gauges is shown to be determined by admissible contractions of the geometrical region considered and a suitable equivalence class of curves is defined. In the special case of magnetostatics, the relevant electromagnetic potentials are directly related to the ponderomotive forces. Schwinger's method of extracting a gauge invariant factor from the fermion propagator could, it is argued, lead to incorrect results. Dirac brackets of both Maxwell and Yang-Mills theories are given for arbitrary admissible space-like paths. It is shown how to define a non-abelian flux and local charges which obey a local charge algebra. Fields associated with the charges differ from the electric fields of the theory by singular topological terms; to avoid this obstruction to the Gauss law it is necessary to exclude a single, gauge fixing curve from the region considered.

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L. Lukaszuk, E. Leader, A. Johansen. 1999-06-03. Contour gauges, canonical formalism and flux algebras. https://doi.org/10.1016/s0550-3213(99)00587-8

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