On the Quantization of Electric and Magnetic Charges and Fluxes. Axiomatic Foundation of Non Integrable Phases. Two Natural Speeds Different from C

Abstract

Peter M. Enders and Rudolf Germer

We present an axiomatic foundation of non-integrable phases of Schrödinger wave functions and use it for interpreting Dirac’s 1931 pioneering article in terms of the electromagnetic 4-potential. The quantization of the electric charge in terms of e implies the quantization of the dielectric flux through closed surfaces Ψ := D · dS in terms of the ‘Lagrangean’ dielectric flux quantum ΨD = e. The quantization of the analogous magnetic monopole charge in terms of g implies the quantization of the magnetic flux through closed surfaces Φ := B· dS in terms of the ‘Diracian’ magnetic induction flux quantum ΦB = g = h/e, and vice versa. Here, the question is raised, if the quantization of the magnetic charge (and hence field) in a given volume depends on the total electric charge in that volume. Furthermore, we have ΦB/ΨD = g/e = h/e2 = RK, the von Klitzing constant, the basic resistance of the quantum Hall effect. RK and the vacuum permittivity ε0 and permeability μ0, respectively, combine to two natural speed constants different from that of light in vacuum c [1.]

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