Clifford Algebra, Geometrization of Interaction and Wave Function Representation

Abstract

The main purpose of this part of the monograph is to present the results of applying a possible approach to the geometric description of elementary particles and the nature of the early universe. Based on the mathematical apparatus of Clifford’s algebra, an approach to geometrization of the theory of elementary particles and interaction is proposed. The novelty lies in the fact that this approach can explain the geometric nature of supersymmetry in terms of the geometric representation of the wave function and propose a mechanism of spontaneous symmetry breaking with different degrees of freedom. It is under such conditions that the well-known spontaneous symmetry breaking occurs and individual excitations acquire mass. Under such conditions, a phase transition occurs with the formation of a new phase with the formation of the universe. The proposed picture more fully reflects the basic approach of geometrization the interaction, which is the basis of the quantum field theory.