On the topological charge concentrated at a point

Abstract

For SU(2) gauge fields over the 4-dimensional sphere with a finite number of points x 1, x 2, ..., and x N removed, there are gauge transformations which modify the topological charge concentrated at x j by adding n j , where n 1, n 2, …, and n N . are integers such that Σ N j = 1 n j = 0. However, the reduction modulo Z of the topological charge at a point is well defined, being given in terms of the secondary characteristic classes of Chern and Simons, except when the topological charge is indeterminate.