| EPSRC Reference: |
GR/R66982/01 |
| Title: |
Topology and Symmetry in High Dimensional Sigma Models |
| Principal Investigator: |
Speight, Professor JM |
| Other Investigators: |
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| Department: |
Pure Mathematics |
| Organisation: |
University of Leeds |
| Scheme: |
Fast Stream |
| Starts: |
01 October 2001 |
Ends: |
30 September 2004 |
Value (£): |
48,498
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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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Study the CPA N models on the 2-sphere; in particular:1. Understand as fully as possible the L^2 geometry of the unit-lump moduli spaces.2. Construct a new family of cohomogeneity 1 Ricci-flat Kaehler metrics on these spaces, or prove non-existence of such a family.3. Investigate exceptionally symmetric multi-lump dynamics within the geodesic approximation.Describe the proposed-research in about 200 words.Static solutions of sigma models are maps between Riemannian manifolds which extremize a geometric energy functional generalizing the Dirichlet energy of harmonic map theory. They model many physical phenomena, including atomic nuclei and topological defects in condensed matter physics. This proposal concerns the Faddeev-Hopf model on non-Euclidean 3-manifolds and the CPA N models on the 2-sphere. For the former, we propose to investigate how the imposition of nontrivial topology on the domain of the model affects its physical content, in both the classical and quantum contexts. For the latter, we propose to study the L^2 geometry of exceptionally symmetric spaces of static solutions, and use this geometry to extract information about classical and quantum CPA N lump dynamics via the method of Manton.
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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 |
| Summary |
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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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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.leeds.ac.uk |