The quantum field theory of electric and magnetic charge

Blagojevic, Sejanovic.

The dynamics of monopoles as quantum objects is described by the quantum field theory of monopoles and charges. Owing to the presence of a preferred direction n, this is the first example of a theory which is not manifestly Lorentz invariant, though intrinsically it possesses this invariance. Another unusual property of this Abelian theory is that it has two coupling constants connected via the quantization condition. The investigation of the basic properties of the theory is facilitated by the existence of various formulations. Thus, Lorentz invariance. which is not easily seen in Schwinger’s Hamiltonian framework, is transparent after the introduction of the particle-path representation of Zwanziger’s local Lagrangian formulation. Ultraviolet properties of the theory receive a superior, n-independent treatment in this representation, with the result that favors opposite renormalization of electric and magnetic charge. The physical content of infrared regularization is clearly described in the one-potential formulation. Several other topics are treated: Dirac’s quantum mechanics of the monopole, connection with non-Abelian monopoles, a supersymmetric generalization of the theory, and its possible role in preon dynamics.