Duality-invariant quantum field theories of charges and monopoles

We present a manifestly Lorentz– and SO(2)–Duality–invariant local Quantum Field Theory of electric charges, Dirac magnetic monopoles and dyons. The manifest invariances are achieved by means of the PST–mechanism. The dynamics for classical point particles is described by an action functional living on a circle, if the Dirac–Schwinger quantization condition for electric and magnetic charges holds. The inconsistent classical Field Theory depends on an arbitrary, but fixed, external vector field, a generalization of the Dirac–string. Nevertheless, the Quantum Field Theory, obtained from this classical action via a functional integral approach, turns out to be independent of the particular vector field chosen, and thus consistent, if the Dirac–Schwinger quantization condition holds. We provide explicit expressions for the generating functionals of observables, proving that they are Dirac–string independent. Since Lorentz–invariance is manifest at each step, the quantum theory admits also a manifestly diffeomorphism invariant coupling to external gravity. Relations with previous formulations, and with SO(2)–non invariant theories are clarified.