In this paper we use the representation method of braid groups to design Feymann integral for the distribution of probability in the problem of plastic deformation in the synergetic formalism. It will allow to see the connection of distribution of probabilities in our paper and the Gauss distribution in papers. | Vietnam Journal of Mechanics, VAST, Vol. 27, No. 4 (2005), pp. 240-244 DEFORMATION OF MEDIUM HAVING STRING STRUCTURE TRINH VAN KHOA Hanoi Architectural University Abstract. In this paper we constructed a model of plastic deformation of the medium having string structure. The knot theory was used to classify the plastic state. 1. INTRODUCTION Knot theory was born in Scotland around the year of 1867. J .C. Maxwell, . Tait and VI. Thomson were the founders of what that has become a knot theory. According to Thomson's theory of chemical elements all atoms are made of small knots formed by vortex lines of either which have to be kinetically stable. After that Alexander has performed the classification of the knot (knot invariant). Now once again knot problem is studding strongly thanks to the results of Jones. In the time one achieves important progress in the mathematics and the physics when one uses knot theory. Concretely, in the paper [1] t he connections between the theory of knot and statistical mechanics are shown and in the theory of knot there is the new device for considering precisely - soluble problem of statistical mechanics . In this c:ase, in the evolutionary equation there is the dynamical symmetry. In simplest case, the determination of invariant of knot is equivalent to determination of function of distribution of probability in a critical point for two-dimension models. Ignoring the strict of mathematical requirement it is equivale1'1t to definition of Feymann integral over a trajectory. That means, every Feymann diagram corresponds a knot invariant. It is the mean idea of \i\Titten. Since, in the Chern-Simons-·wit ten theory the statistical sum is covariant - equivalent to knot invariant ( "Link invariant") . A matter of course, the Wilson line was identified with a strings . In research of two-dimension model a condition of integrability is connected to a subgroup of braid group (in the Yang-Baxter equation). What do we receive when we use .
