Electromagnetic coupling of strongly non-local quantum mechanics

Abstract

Although standard quantum mechanics has some non-local features, the probability current of the Schrödinger equation is locally conserved, and this allows minimal electromagnetic coupling. For some important extensions of the Schrödinger equation, however, the probability current is not locally conserved. We show that in these cases the correct electromagnetic coupling requires a relatively simple extension of Maxwell theory which has been known for some time and recently improved by covariant integration of a scalar degree of freedom. We discuss some general properties of the solutions and examine in particular the case of an oscillating dipolar source. Remarkable mathematical and physical differences emerge with respect to Maxwell theory, as a consequence of additional current terms present in the equations for $\nabla \cdot \text{E}$ and $\nabla \times \text{B}$. Several possible applications are mentioned.

arXiv comment10 pages, 2 figures

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• Are current discontinuities in molecular devices experimentally observable?
• High-frequency electromagnetic emission from non-local wavefunctions
• Generalized local charge conservation in many-body quantum mechanics
• Do we need an alternative to local gauge coupling to electromagnetic fields?
• Quantum uncertainty and energy flux in extended electrodynamics