Derivation of the Selected Path Integral

概要

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To analyze the generalized Brownian motion, i.e. the fractional Brownian motion, we propose a path integral which is governed by the modified action along the principal path with fractal natures, i.e. mainly observable path in a diffusive phenomena. By modified the definition of the action and summing over fractal paths, the path integral is derived . We investigate several properties of this integral. The principal path has a fractal structure and the path integral represents the transition probability of the fractional Brownian motion. The transition probability itself has no dependence on the structure of principal paths. The path integral is mainly characterized by two parameters, the Hausdorff dimension D_H of principal paths representing a microscopic structure and the Hurst coefficient H representing a macroscopic structure, which are independent of each other.
社団法人日本物理学会の論文
1995-11-15