Abstract
Recently by using path integral method and theory of soliton, a new calculation scheme of a partition function of an immersion object has been proposed [J. Phys. A 31 (1998) 2705–2725]. In this paper, the scheme to elastica (space curve with the Bernoulli-Euler functional) immersed in three-dimensional space R 3 as a physical model in polymer science is applied. It is shown that the nonlinear Schrödinger and complex modified Korteweg-de Vries hierarchies naturally appear to express the functional space of the partition function. In other words, it is shown that the configuration space of an elastica immersed in R 3 can be classified by these equations. Then the partition function is reduced to an ordinary integral over the orbit space of these hierarchies.
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