Duality-invariant Quantum Field Theories of Charges and Monopoles

TL;DR

This paper develops a Lorentz- and SO(2)-duality-invariant quantum field theory for electric charges, monopoles, and dyons, ensuring consistency and independence from arbitrary string choices through the PST mechanism.

Contribution

It introduces a manifestly invariant local quantum field theory using the PST mechanism that unifies electric and magnetic charges with consistent quantization and independence from Dirac-string choices.

Findings

Quantum theory is independent of the Dirac-string choice.

The classical action on a circle reproduces the quantum invariance.

The theory is compatible with external gravity and diffeomorphism invariance.

Abstract

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.