Topological gauge fixing II: A homotopy formulation

Abstract

We revisit the implementation of the metric-independent Fock–Schwinger gauge in the Abelian Chern–Simons field theory defined in ℝ3 by means of a homotopy condition. This leads to the Lagrangian [Formula: see text] in terms of curvatures F and of the Poincaré homotopy operator h. The corresponding field theory provides the same link invariants as the Abelian Chern–Simons theory. Incidentally the part of the gauge field propagator which yields the link invariants of the Chern–Simons theory in the Fock–Schwinger gauge is recovered without any computation.