ELECTROMAGNETISM AND MULTIPLE-VALUED LOOP-DEPENDENT WAVE FUNCTIONALS

Abstract

We quantize the Maxwell theory in the presence of an 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 for 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.