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The exact connection between the feynman integral and a completely integrable system

Abdul Aziz, Zainal (2005) The exact connection between the feynman integral and a completely integrable system. Project Report. Universiti Teknologi Malaysia. (Unpublished)

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Abstract

We review recent attempts to relate the concept of Feynman integral and integrable systems. This constitutes an endeavour on our part in making the Feynman path integral into a mathematically meaningful entity. We then presents a framework which is 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 systems. This idea originates primarily from Witten’s (1991) conjecture and Kontsevich’s (1992) model which conjecturally able to formulate this remarkable connection. Essentially this link refers to a generator function of intersection numbers on moduli space for stable curves (or r-spin curves) and the taufunction of Korteweg-de Vries (or Gelfand-Dikii) hierarchy. In order to display the calculational aspects of this deliberation, certain special models with superpotentials are examined.

Item Type:Monograph (Project Report)
Uncontrolled Keywords:exact connection, the feynman integral, a completely integrable system.
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:2878
Deposited By: Nor Azlin Nordin
Deposited On:21 May 2007 00:20
Last Modified:22 May 2012 03:41

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