Manifest gauge and Poincaré covariance

Abstract

Manifest gauge invariance is known to be incompatible with manifest Poincaré covariance (Strocchi's theorem). By extending the notion of gauge invariance to that of gauge covariance, we circumvent that incompatibility, at least for free electromagnetic potentials. In the new formulation the potentials, A G , for all permissible gauges G. act on a common Hilbert space. This formulation is shown to be inequivalent to the more conventional ones. (In particular, the Coulomb gauge is now inaccessible.) The abstract gauges G are represented by c-number potentials V G , which play a central role in the theory. Even without interaction, they obey a field equation with a source, and thus they anticipate the existence of electric charges.