Kamiran Feynman dan sistem terkamir lengkap: kerangka kerja baru dalam matematik fizik (Feynman integral and completely integrable system: a new framework in mathematical physics)

Abstract

This paper presents briefly a new framework in mathematical physics. This is well rooted in the hypothetical relationship between the heuristic concept of Feynman integral in physics and the rigorous mathematical results derived from the theory of (physically significant) completely integrable (hierarchical) systems. The idea originates primarily from Witten?s (1991) conjecture and Kontsevich?s (1992) model which systematically able to formulate this remarkable connection. Essentially this link refers to a generator function of intersection numbers on moduli space for stable curves (or more generally r-spin curves) and the tau-function of Korteweg-de Vries (or Gelfand-Dickey) hierarchy. This research direction is further elaborated.