Remarks on Zwanziger's local quantum field theory of electric and magnetic charge

Various aspects of Zwanziger's local Lagrangian formulation of a relativistic quantum field theory of electric and magnetic charge are investigated with a view toward determining the consistency of the theory. A slight generalization of the classical particle theory is first studied and shown to be equivalent to the more-familiar nonlocal formulations due to Yan and Schwinger and to Dirac. The actions for each of these theories must first be altered so that the correct Lorentz force law results even if a charged-particle trajectory intersects a solenoidal "string" attached to each monopole. The resultant actions are then seen to be invariant under combined string rotations and (singular) gauge transformations. The duality invariance (i.e., invariance under interchange of electric and magnetic quantities) of these theories is also discussed. For the quantum field theory, it is shown how the boundary conditions are to be chosen so that one has rotational invariance about the string direction $\hat{n}$, boost invariance along $\hat{n}$, and duality invariance. The condition for full Lorentz invariance is discussed and it is argued that the Lorentz invariance of the classical and first-quantized theories suggests what is necessary in order that the quantum field theory is also Lorentz invariant. The Feynman rules for the theory are confirmed from the Faddeev-Popov ansatz, and their unitarity is explicitly verified. It is also shown that there are no unphysical intermediate states (if duality invariance is maintained), that the bare electric and magnetic charges are renormalized by the same factor, and that the theory is infrared-free.