Quantum Field Theory of Particles with Both Electric and Magnetic Charges

TLDR

The paper extends Schwinger's quantum field theory to include particles carrying both electric and magnetic charges. The authors prove a chiral equivalence theorem linking systems with mixed charges and show that charge quantization applies to combinations of electric and magnetic charges, implying the existence of a second elementary electric charge on the Dirac monopole.

Abstract

The quantum field theory of particles with both electric and magnetic charges is developed as an obvious extension of Schwinger's quantum field theory of particles with either electric or magnetic charge. Two new results immediately follow. The first is the chiral equivalence theorem which states the unitary equivalence of the Hamiltonians describing the system of particles with electric and magnetic charges ${e}_{n}$, ${g}_{n}$ and the system with charges ${{e}_{n}}^{\ensuremath{'}}=cos\ensuremath{\theta}$, ${e}_{n}+sin\ensuremath{\theta}{g}_{n}$, ${{g}_{n}}^{\ensuremath{'}}=\ensuremath{-}sin\ensuremath{\theta}{e}_{n}+cos\ensuremath{\theta}{g}_{n}$. This result holds in particular in the absence of physical magnetic charges. The second result is that if physical magnetic charges do occur, then, in consequence of chiral equivalence, the charge quantization condition applies, not to the separate products ${e}_{m}{g}_{n}$, but to the combinations ${e}_{m}{g}_{n}\ensuremath{-}{g}_{m}{e}_{n}$, which must be integral multiples of $4\ensuremath{\pi}$. The general solution of this condition leads to the introduction of a second elementary quantum of electric charge ${e}_{2}$, the electric charge on the Dirac monopole, besides the first elementary charge ${e}_{1}$, the charge on the electron. There are no other free parameters.