Nonlinear Phenomena in Complex Systems, 2002, Vol.5, No.1, pp.95-107

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2002, Vol.5, No.1, pp.95-107

The Structure of Singularities and Gauge Principle
V.M.Red'kov

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 themost preferable one. The paper aims to analyze this view by interpreting themonopole situation in terms of conventional Fourier series theory; in particular, having relied on the Dirichlet theorem. It is shown that themonopole case can be labelled as avery specific and even rather simple class of problems in theframe of that theory: all three monopole gauges amount to practically thesame one-dimensional problem for functions given on the interval [0, Pi], having asingle point of discontinuity; these three vary only in its location. Some general aspects of the Aharonov-Bohm effect are discussed; also the way of how any singular potentials such as monopole's, being allowed in physics, affect the essence of the physical gauge principle itself is considered.
Key words: Monopole, singularity, Dirichlet theorem, gauge principle

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