EPSRC Reference: 
EP/H000054/1 
Title: 
Nonultralocality and new mathematical structures in quantum integrability 
Principal Investigator: 
MacKay, Professor NJ 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of York 
Scheme: 
Standard Research 
Starts: 
01 October 2009 
Ends: 
31 March 2013 
Value (£): 
352,347

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
03 Jun 2009

Mathematics Prioritisation Panel June 2009

Announced


Summary on Grant Application Form 
The crucial natural question to ask of a problem in mathematical physics is whether we can solve it. Since most such problems are couched in the language of differential equations, the question is therefore of whether we can integrate the equations, of whether the problem is 'integrable'. The generalized mathematics of integrability is that of the structures which make some problems solvable in a way that others are not. Perhaps surprisingly, it turns out that fundamental physics makes much use of integrable models. The mathematical analysis of the central issue in modern fundamental physics, the relationship between the gauge theories of particle physics and the much more speculative string theory (the 'gauge/string correspondence'), has proved to be full of integrable models in recent years  but whereas conventional integrability refers to timeevolution, the crucial integrability in gauge theory is with the evolution of the energy scale.Some integrable models are 'ultralocal'  that is, very wellbehaved in terms of the localization of their interactions. Most of the mathematical techniques of quantum integrability apply principally to such models. Less wellbehaved, 'nonultralocal' (nonUL) models are harder to handle, but keep reappearing and increasing in importance. Sometimes their problems can be accommodated in a rather adhoc way, but a systematic understanding of them is lacking. This project attacks the problem from a number of directions. Some involve attempting to understand better the algebraic structures underlying known nonUL models, with or without a boundary, especially those of, or generalized from, the gauge/string correspondence. However, a new departure is to take existing ideas for handling nonUL models in the abstract and attempt 'reverseengineer' the associated nonUL integrable models.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


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Project URL: 
http://gow.epsrc.ac.uk/ViewGrant.aspx?GrantRef=EP/H000054/1 
Further Information: 

Organisation Website: 
http://www.york.ac.uk 