Electromagnetism and multiple-valued loop-dependent wave functionals

TL;DR

This paper explores the quantization of Maxwell's theory with electric charges using a dual loop representation, revealing that the wave functional becomes multivalued due to the configuration space's topology.

Contribution

It introduces a dual loop representation for Maxwell theory with electric charges, highlighting the multivalued nature of wave functionals as a topological effect.

Findings

Wave functional becomes multivalued in the dual loop representation.

Multivaluedness arises from the multiply-connected configuration space.

Dual representation provides new insights into electromagnetic quantization.

Abstract

We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that the theory can be seen as a theory without sources, except by the fact that the wave functional becomes multivalued. This can be seen as the dual counterpart of what occurs in Maxwell theory with a magnetic pole, when it is quantized in the ordinary Loop Representation. The multivaluedness can be seen as a result of the multiply-connectedness of the configuration space of the quantum theory.