A phase cell approach to Yang-Mills theory V. Analysis of a chunk

Abstract

In the present formalism the Yang-Mills field is constructed as a “non-linear sum” of excitations, small field excitations, the modes, and large field excitations, the chunks. The chunk excitations, herein studied, are each described by a finite number of group element variables. The continuum field associated to the excitation in general has point gauge singularities (arising from the non-trivial π₃(G)). We find estimates for plaquette assignments, edge assignments, and the smoothness of edge assignments, at all scales. The central conceptual motor in our constructions and estimates is a split up of the field at each length scale, locally, into a pure gauge field, and a deviation field. An example is presented establishing the general inevitability of gauge singularities, as a consequence of fall off requirements on the continuum field of an excitation.