SPACE, TIME AND FUNDAMENTAL INTERACTIONS

RELATIONAL DESCRIPTION OF ELECTROWEAK INTERACTIONS

Vladimirov Yu.S., Tereshchenko D.A.

The binary pregeometry was used as a mathematical basis for the relational approach. The description of electroweak interactions of elementary particles is realized by binary systems of complex relations of rank (4, 4). In this paper, we show that there are three variants for writing a basic \(4 \times 4\)-relation. In this cases, the basic \(4 \times 4\)-relation is represented as a square of the \(SL(2,C)\) invariant. This invariant constructed from two 2-component spinors formed from elements of bound particles. One of these variants was used to describe the electromagnetic interaction of two particles in the relational statistical theory of a hydrogen atom. Two other variants are characterized by mixing in 2-component spinors of left and right components of particles in the bound state. These variants are proposed to be used to describe a simplified model of electroweak decay. Bound and unbound states of elementary particles were described in the framework of different geometries, which had been mentioned by V. A. Fock for \(O\)(4) symmetry in the hydrogen-like atom problem.