Measure of irregularity for Dirac, Schwinger, Wu-Yang's bases in the Abelian monopole theory and affecting of the gauge symmetry principle by allowance of singularity in physics

Abstract

In the literature concerning the monopole matter, three gauges: Dirac, Schwinger, and Wu-Yang's, have been contrasted to each other, and the Wu-Yang's often appears as the most preferable one. The article aims to analyse this view by interpreting the monopole situation in terms of the conventioal Fourier series theory; in particular, having relied on the Dirichlet theorem. It is shown that the monopole case can be labelled as a very spesific and even rather simple class of problems in the frame of that theory: all the three monopole gauges amount to practicaly the same one-dimentional problem for functions given on the interval [0,pi] having a single point of discontinuity; these three vary only in its location.In addition, some general aspects of the Aharonov-Bohm effect are discussed; the way of how any singular potentials such as monopole's, being allowed in physics, touche the essence of the physical gauge principle itself is considered.