The Feymann integral and completely integrable systems
We review recent attempts to relate the concept of Feynman integral with integrable systems. We then present a framework which is rooted in the hypothetical relationship between the heuristic concept of Feynman integral in theoretical physics and the rigorous mathematical results derived from the th...
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| Format: | Book Section |
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Penerbit UTM
2007
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| _version_ | 1796855350758998016 |
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| author | Abdul Aziz , Zainal |
| author_facet | Abdul Aziz , Zainal |
| author_sort | Abdul Aziz , Zainal |
| collection | ePrints |
| description | We review recent attempts to relate the concept of Feynman integral with integrable systems. We then present a framework which is rooted in the hypothetical relationship between the heuristic concept of Feynman integral in theoretical physics and the rigorous mathematical results derived from the theory of (physically signi?cant) completely integrable systems. This idea originates primarily from Witten’s conjecture and Kontsevich’s 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 tau-function of Korteweg-de Vries (or Gelfand-Dikii) hierarchy. Based on Witten-Kontsevich’s result, we also discuss the idea of recasting the tau function in terms of the Feynman diagrams. |
| first_indexed | 2024-03-05T18:27:20Z |
| format | Book Section |
| id | utm.eprints-14163 |
| institution | Universiti Teknologi Malaysia - ePrints |
| last_indexed | 2024-03-05T18:27:20Z |
| publishDate | 2007 |
| publisher | Penerbit UTM |
| record_format | dspace |
| spelling | utm.eprints-141632011-08-18T09:28:58Z http://eprints.utm.my/14163/ The Feymann integral and completely integrable systems Abdul Aziz , Zainal Q Science (General) We review recent attempts to relate the concept of Feynman integral with integrable systems. We then present a framework which is rooted in the hypothetical relationship between the heuristic concept of Feynman integral in theoretical physics and the rigorous mathematical results derived from the theory of (physically signi?cant) completely integrable systems. This idea originates primarily from Witten’s conjecture and Kontsevich’s 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 tau-function of Korteweg-de Vries (or Gelfand-Dikii) hierarchy. Based on Witten-Kontsevich’s result, we also discuss the idea of recasting the tau function in terms of the Feynman diagrams. Penerbit UTM 2007 Book Section PeerReviewed Abdul Aziz , Zainal (2007) The Feymann integral and completely integrable systems. In: Recent Advances In Theoretical and Numerical Methods. Penerbit UTM , Johor, pp. 57-80. ISBN 978-983-52-0610-8 |
| spellingShingle | Q Science (General) Abdul Aziz , Zainal The Feymann integral and completely integrable systems |
| title | The Feymann integral and completely integrable systems |
| title_full | The Feymann integral and completely integrable systems |
| title_fullStr | The Feymann integral and completely integrable systems |
| title_full_unstemmed | The Feymann integral and completely integrable systems |
| title_short | The Feymann integral and completely integrable systems |
| title_sort | feymann integral and completely integrable systems |
| topic | Q Science (General) |
| work_keys_str_mv | AT abdulazizzainal thefeymannintegralandcompletelyintegrablesystems AT abdulazizzainal feymannintegralandcompletelyintegrablesystems |