| EPSRC Reference: |
GR/N27330/01 |
| Title: |
ORDINARY DIFFERENTIAL EQUATIONS INTEGRABLE QUANTUM FIELD THEORIES |
| Principal Investigator: |
Dorey, Professor P |
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| Department: |
Mathematical Sciences |
| Organisation: |
Durham, University of |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 November 2000 |
Ends: |
31 October 2001 |
Value (£): |
40,128
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Physics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The proposed research grows out of an observation made a little over a year ago by the VF and the proposer, and subsequently developed both by them and by a number of other authors. This observation established a link between certain ordinary differential equations in the complex domain, and certain Bethe ansatz systems and associated integral equations which have arisen in integrable quantum field theory. So far, details have only been fully worked out for cases related to the Lie algerbras A1 and A2, but the preliminary results indicate that a generalisation to An is possible. By completing this task we expect to understand more of the underlying mathematical structures, which we hope will enable us to find similar correspondences at least for the remaining simply-laced Lie algebras, of types D and E, and perhaps also for Bethe ansatz systems related to lattice models, and a further line of investigation will explore whether anything similar exists for the excited states. The correspondence offers the prospects of new insights into both integrable models and ordinary differential equations, and while working on the general picture the VF will also seek applications to concrete problems, one such being the treatment of boundary effects in integrable quantum field theories.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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