# Covariant formulation of Aharonov-Bohm electrodynamics and its application to coherent tunnelling

## TL;DR

This paper reformulates Aharonov-Bohm electrodynamics covariantly, revealing its ability to handle non-conserved sources and its implications for quantum tunneling and condensed matter systems.

## Contribution

It presents a covariant formulation of extended electrodynamics that accommodates non-conserved sources and explores its applications to quantum tunneling and fractional quantum systems.

## Key findings

- The theory allows sources with non-conserved current to generate observable fields.
- Microscopic charge violations are effectively 'censored' at the macroscopic level.
- Potential applications to condensed matter systems with quantum tunneling are discussed.

## Abstract

The extended electrodynamic theory introduced by Aharonov and Bohm (after an earlier attempt by Ohmura) and recently developed by Van Vlaenderen and Waser, Hively and Giakos, can be re-written and solved in a simple and effective way in the standard covariant 4D formalism. This displays more clearly some of its features. The theory allows a very interesting consistent generalization of the Maxwell equations. In particular, the generalized field equations are compatible with sources (classical, or more likely of quantum nature) for which the continuity/conservation equation $\partial_\mu j^\mu=0$ is not valid everywhere, or is valid only as an average above a certain scale. And yet, remarkably, in the end the observable $F^{\mu \nu}$ field is still generated by a conserved effective source which we denote as $(j^\nu+i^\nu)$, being $i^\nu$ a suitable non-local function of $j^\nu$. This implies that any microscopic violation of the charge continuity condition is "censored" at the macroscopic level, although it has real consequences, because it generates a non-Maxwellian component of the field. We consider possible applications of this formalism to condensed-matter systems with macroscopic quantum tunneling. The extended electrodynamics can also be coupled to fractional quantum systems.

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Source: https://tomesphere.com/paper/1702.02026