Field-strength and dual variable formulations of gauge theory

Abstract

Using completely fixed axial-like gauges, I construct the unique inversion $A\left(F\right)\mathrm{}$ for the potential $A$ in terms of the field strength $F$. A change of variable to $F$ results in a field-strength formulation of gauge theory. $F$ is constrained to satisfy the Bianchi "identities" $\partial \tilde{F}-eA\left(F\right)\mathrm{}\tilde{F}=0\mathrm{}$. Dual potentials $\tilde{A}$ may also be introduced as functional Fourier conjugates to the Bianchi forms. For quantum electrodynamics in four dimensions, duality ($F\to \tilde{F}$, $A\to \tilde{A}$) is a perfect symmetry. However, residuals of the symmetry persist in all theories: E.g., Gauss's law is an identity; $\tilde{A}$ is canonical to the magnetic fields, and closely related to 't Hooft's disorder operators. DOI: http://dx.doi.org/10.1103/PhysRevD.19.517 © 1979 The American Physical Society