Statistical mechanics of non-stretching elastica in three-dimensional space

Recently by using path integral method and theory of soliton, a new calcula tion scheme of a partition function of an immersion object has been propose d [J. Phys. A 31 (1998) 2705-2725]. In this paper, the scheme to elastica ( space curve with the Bernoulli-Euler functional) immersed in three-dimensio nal space [R-3 as a physical model in polymer science is applied. It is sho wn that the nonlinear Schrodinger and complex modified Korteweg-de Vries hi erarchies naturally appear to express the functional space of the partition function. In other words, it is shown that the configuration space of an e lastica immersed in R-3 can be classified by these equations. Then the part ition function is reduced to an ordinary integral over the orbit space of t hese hierarchies. (C) 1999 Elsevier Science B.V. All rights reserved.