Theory of the non-linear

The non-linear wave theory,

adequate of Standard Model

Alexander G. Kyriakos

St. Petersburg, Russia.

E-mail: a.g.kyriak@hotmail.com

agkyriak@hol.gr

Annotation

The theory of non-linear wave, whose objects are identical to the elementary particles, is presented here. The last development of physics predicts the possibility of such type of elementary particle theory, as, for example, it follows from the below quotation.

“No-one can deny success which quantum field theory, in the perturbative approximation, has enjoyed over the last half century… Yet despite these successes, the question of how to describe the basic matter fields of nature has remained unanswered –except, of course, through the introduction of quantum number and symmetry groups. As far as field theory goes, the matter fields are treated as point objects. Even in classical field theory these present us with unpleasant problems, in the shape of the infinite self-energy of a point charge. In the quantum theory, these divergences do not disappear; on the contrary, they appear to get worse, and despite the comparative success of renormalization theory the feeling remains that there ought to be a more satisfactory way of doing things.

Now it turns out that non-linear classical field theories possess extended solutions, commonly known as solitons, which represent stable configurations with a well-defined energy which is nowhere singular. May this be of relevance to particle physics? Since non-Abelian gauge theories are non-linear, it may well be, and the last ten years have seen the discovery of vortices, magnetic monopoles and instantons, which are soliton solutions to the gauge-field equations in two space dimensions (i.e. a ‘string’ in 3- dimensional space), three space dimensions (localized in space but not in time) and 4-dimensional space-time (localized in space and time). If gauge theories are taken seriously then so must these solitions be. It will be seen that they do give rise to new physics and there is even the hope that they may solve the problem of quark confinement.” (L. H. Rayder. The quantum field theory. 1985. Chapter 10. Topological objects in field theory).

Such attempt of “soliton” or “vortex” description of elementary particles is presented below. Here it is shown that the soliton solutions actually have several classes, like the mentioned types in the quotation, to which correspond different families of elementary particles. Moreover in two last classes, where the problem of confinement appears, the solutions are found namely as a problem of non-linear wave theory.

The objects of the proposed theory do not have analogs in classical physics, which makes it possible to explain the gap between the classical and quantum theories. The theory allows to clarify the origin and to calculate many characteristics, inherent in real elementary particles.