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

摘要

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'soften appears as the most preferable one. The article aims to analyse this viewby interpreting the monopole situation in terms of the conventioal Fourierseries theory; in particular, having relied on the Dirichlet theorem. It isshown that the monopole case can be labelled as a very spesific and even rathersimple class of problems in the frame of that theory: all the three monopolegauges amount to practicaly the same one-dimentional problem for functionsgiven on the interval [0,pi] having a single point of discontinuity; thesethree vary only in its location.In addition, some general aspects of theAharonov-Bohm effect are discussed; the way of how any singular potentials suchas monopole's, being allowed in physics, touche the essence of the physicalgauge principle itself is considered.