| EPSRC Reference: |
GR/A90428/02 |
| Title: |
SYMMETRY AND DUALITY AS KEYS FOR UNRAVELLING THE DYNAMICS OF QUANTISED GANGE THEORIES |
| Principal Investigator: |
Schroers, Professor B |
| Other Investigators: |
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| Department: |
S of Mathematical and Computer Sciences |
| Organisation: |
Heriot-Watt University |
| Scheme: |
Advanced Fellowship (Pre-FEC) |
| Starts: |
01 September 2000 |
Ends: |
31 August 2004 |
Value (£): |
182,864
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Summary on Grant Application Form |
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Symmetry considerations play an essential role in the mathematical analysis of physical phenomena. At a practical level they allow for important simplifications in the analysis of dynamical systems. However, in many `branches of mathematical physics symmetry plays a more profound role, and this is particularly true in the study of quantised gauge theories. Such theories play an important role in both physics and mathematics, providing on the one hand the central building blocks for modern theories of elementary particles and on the other new insights into deep problems in geometry and topology. This proposal addresses aspects of two particularly prominent gauge theories, namely Yang-Mills theory and Chern-Simons theory. Yang-Mills theory, a non-linear generalisation of Maxwell's electrodynamics, contains electric and magnetic excitations. While there is a manifest symmetry among the electric degrees of freedom there is a more mysterious and hidden symmetry among the magnetic degrees of freedom. Furthermore there has long been conjectured to be a duality between the electric and the magnetic symmetry of the theory. A fascinating aspect of this duality is that it involves quantum theory in an essential way. The first half of this proposal addresses this duality of symmetries. It aims to clarify structural aspects but also to exploit duality to shed light on dynamcal question which are not accessible by current methods. In the second half we consider Chern-Simons theory. This provides a further example of a theory which, at the quantum level, displays a surprising form of symmetry. Here the appropriate mathematical theory is that of quantum groups. While understanding symmetry and duality in Yang-Mills theory facilitates the exploration of the dynamics, it is fair to say that in Chern-Simons theory knowing the symmetry answers essentially all dynamcal questions. This is the motivation for addressing, in the second half of the proposal, a class of Chern-Simons theories for which the appropriate quantum group is either little studied or unkown. These theories are related to quantum gravity in (2+1) dimensions and are therefore particularly intriguing.
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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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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.hw.ac.uk |