Fiber bundle structure analysis and its application to the magnetic monopoles

Abstract

Using the idea "Pastes" which is known to mathematicians as "Sets of transition functions", fiber bundle and differential geometric languages are re-defined. In terms of these, possible similarities between the gauge theories and the fiber bundle theories are systemetically discussed. In this work, all fiber bundle types over the Minkowski space-time with n time like infinite string singularities are rigorously determined. It is shown that if the structure group G is arcwise connected, the types of monopoles are determined by n direct sum of the first homotopy group $\pi_1(G)$ of G.