Gauge waves generation and detection in Aharonov–Bohm electrodynamics

Abstract

The extended Aharonov–Bohm electrodynamics has a simple formal structure and allows to couple the e.m. field also to currents which are not locally conserved, like those resulting from certain non-local effective quantum models of condensed matter. As it often happens in physics and mathematics when one tries to extend the validity of some equations or operations, new perspectives emerge in comparison to Maxwell theory, and some “exotic” phenomena are predicted. For the Aharonov–Bohm theory the main new feature is that the potentials $$A^\mu $$ A μ become univocally defined and can be measured with probes in which the “extra-current” $$I=\partial _\mu j^\mu $$ I = ∂ μ j μ is not zero at some points. As a consequence, it is possible in principle to detect pure gauge-waves with $${\textbf{E}}={\textbf{B}}=0$$ E = B = 0 , which would be regarded as non-physical in the Maxwell gauge-invariant theory with local current conservation. We discuss in detail the theoretical aspects of this phenomenon and propose an experimental realization of the detectors. A full treatment of wave propagation in anomalous media with extra-currents and of energy–momentum balance issues is also given.

Simple circuit and experimental proposal for the detection of gauge-waves

“…Along the oscillation axis of the dipole we have that A T = 0, so that the wave is longitudinal and a pure gauge wave [1]. At any other point, the four-potential can be considered as the sum of a gauge wave (f, A n ) and a transverse vector potential (0, A T ).…”

“…The general principle for computing the effect of a gauge wave on an anomalous conductor is the following [1]. Suppose that in the absence of the wave the conductor hosts a certain unperturbed current density j u and unperturbed electric field E u .…”

“…The constant γ depends on the material and is defined in the phenomenological 'γ-model' [1]; a characteristic relation involving γ is the generalized continuity equation…”

“…Their tunneling dynamics is related to Klein tunneling, in which local charge conservation is not ensured ([21-24] and refs. ; see also [1] for more details).…”

“…In the following, we shall write in parentheses the compact relativistic version of some of the equations, in order to facilitate comparisons among different references. For equation (1) the relativistic version is:…”