This article examines how the physical presence of field energy and particulate matter could influence the topological properties of space time. The theory is developed in terms of vector and matrix equations of exterior differential forms. The topological features and the dynamics of such exterior differential systems are studied with respect to processes of continuous topological evolution. The theory starts from the sole postulate that field properties of a Physical Vacuum (a continuum) can be defined in terms of a vector space domain, of maximal rank, infinitesimal neighborhoods, that supports a Basis Frame as a 4 x 4 matrix of C2 functions with non-zero determinant. The basis vectors of such Basis Frames exhibit differential closure. The particle properties of the Physical Vacuum are defined in terms of topological defects (or compliments) of the field vector space defined by those points where the maximal rank, or non-zero determinant, condition fails. The topological universality of a Basis Frame over infinitesimal neighborhoods can be refined by particular choices of a subgroup structure of the Basis Frame, [B]. It is remarkable that from such a universal definition of a Physical Vacuum, specializations permit the deduction of the field structures of all four forces, from gravity fields to Yang Mills fields, and associate the origin of topological charge and topological spin to the Affine torsion coefficients of the induced Cartan Connection matrix [C] of 1-forms.
Download