Topological Solitons in Discrete Space-Time as the Model of Fermions

Abstract

In the present paper we discuss arguments, favouring the view that massive fermions represent dislocations (i.e. topological solitons) in discrete space-time with Burgers vectors, parallel to an axis of time. If to put symmetrical parts of tensors of distortions (i.e. derivatives of atomic displacements on coordinates) and mechanical stresses equal zero, the equations of the field theory of dislocations get the form of the Maxwell equations. If to consider these tensors as symmetrical, we shall receive the equations of the theory of gravitation, and it turns out that the sum of tensor of distortions and pseudo-Euclidean metrical tensor is the analogue of metrical tensor. It is shown that we can also get Dirac equation with four-fermion interaction in the framework of the field theory of dislocations. This model explains quantization of electrical charge: it is proportional to the topological charge of dislocation, and this charge accepts quantized values because of discrete structure of the 4-dimensional lattice.