The God has created a man in order that he creates that the God fails to do

Wednesday, 19 October 2011

The prespinor model (from my Scientific Biography)

My Scientific Biography: ...Nevertheless, the most promising of my nominated ideas was a model of prespinors (which however till now remains only "promising").

It is known that the root diagrams of simple complex Lie algebras admit groups of reflections, which are finite Coxeter groups. Moreover, the classification of simple complex Lie algebras and their real subalgebras is conducted by means of finite Coxeter groups. They are groups of symmetries of the weight diagrams of irreducible representations of these Lie algebras, which the algebras both of internal and space-time symmetries belong to.

There was an idea that Lie algebras and groups of symmetries can be replaced with the corresponding finite Coxeter groups. Generating elements s of these groups have the property ss=1, and the diversity of these groups is due to the fact that different generating elements do not commute between themselves. The simplest Coxeter group consists of two elements (s,1) and serves as a symmetry group of a 2-spinor. Let us suppose that a physical world in its basis is made of such spinors, let us call them the  prespinors, so that, when their interaction, Coxeter groups of their transformations become non-commutative, providing all the known diversity of symmetries of elementary particles. Moreover, we can go even further and identify elements of the simple Coxeter group (s,1) with the simplest logical system of statements ("no", "yes").

D.Ivanenko believed this model to be very promising. He saw in it the prospect of a continuation of Heisenberg’s and his unified nonlinear field theory, which by that time had stepped aside in the light of theory of gauge fields. It became clear that an interaction of elementary particles is described by exchange of mediators, gauge fields, but not nonlinearities, though not everywhere. For example, an interaction of a field of Cooper pairs in the theory of superconductivity is due to non-linearity, and it may happen that an interactions of a Higgs fields and prespinors are of this type.

The  prespinor model is presented in our book  "
Gravitation" (1985) (in Russ.) and a few articles,  but no further development has obtained, since it is unclear how to describe the dynamics of systems with finite groups of symmetries.


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