2017/10/09 by Alfred S. Goldhaber, Goldhaber, Alfred Scharff, Ricardo Heras +1
Physics and Astronomy · #FOS: Physical sciences #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1710.03321
openalex publication_date 2017/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dirac in 1931 gave a beautiful argument for the quantization of electric charge, which required only the existence in the universe of one magnetic monopole, because gauge invariance of the interaction between the pole and any charge could hold only if the product of the charge and the pole strength were quantized in half-integer multiples of the reduced Planck constant. However, if the photon had a nonzero mass, implying exponential decrease of the flux out of an electric charge, then Dirac's argument might seem to fail. We demonstrate that the result still should hold. The key point is that magnetic charge, unlike electric charge, cannot be screened, so that on any surface enclosing the pole Dirac's string, or equally the Wu-Yang gauge shift, must be present, and to make either of these invisible to charged particles the quantization condition is required.