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Nonperturbative methods: from quantum field theory to condensed matter physics

Ziel

The present project involves several groups of researchers known for their considerable contributions to nonperturbative methods in quantum field theory and condensed matter physics. The main aim of the project is to promote collaboration between these groups. The financial support of the research activities of the NIS groups as a rule will be given in a form of individual grants for their teams' members.
The objectives of the projects includes studying of duality for classical and quantum many-body integrable systems inspired by duality in gauge theories and modern development of D-branes theory. Another point is investigating of geometric nature of symplectic structures on moduli spaces appearing as phase spaces of physical theories, and subsequent quantization of the moduli spaces. The description of the resulting Hilbert spaces, which are spaces of states of the corresponding quantum theories, is expected to be obtained in terms of quantum groups. Solutions of the Knizhnik-Zamolodchikov(-Bernard) equations and their quantized (difference) counterparts should be relevant to the description. An important direction of the project is studying of the SU(N) Yang-Mills theory in dual variables, recently suggested in connection with constructing knotted soliton-like configurations. In application to condensed matter physics transport of two-dimensional carriers is to be investigated as well as some aspects of fractional quantum Hall theory are to be worked out.

The joint research activity will be basically in the form of exchange of scientists, exchange of results and joint participation of researchers from different teams in conferences and workshops.

The following results are expected to be obtained:
1. Mathematical background for the quantum analogue of Ruijsenaars "action-angle" map. Relations between duality in integrable systems and discrete Fourier transform;

2. The r-matrix approach and separation of variables in the difference analogue of Hitchin systems;

3. Quantization of the space of Quasifuchsian groups;

4. Construction of quantum Chern-Simons theories with non-compact gauge groups;

5. q-Hypergeometric solutions for the quantized Knizhnik-Zamolodchikov(-Bernard) equations associated with the Lie algebra gl(N);

6. The functional integral formalism for the SU(N) Yang-Mills theory in dual variables;

7. Deformations of quantum integrable models under twist transformations;

8. Classical and quantum transport of two-dimensional carriers in a smooth random potential or a random magnetic field.

9. Extended analysis of drag and optical effects in double layer systems with correlated disorder;

10. Tunnelling into the fractional quantum Hall liquid.

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Koordinator

Uppsala University
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Adresse
Lagerhyddsvagen Hus 19
75108 Uppsala
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Beteiligte (5)

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Letzte Aktualisierung: 30 Oktober 2002

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Permalink: https://cordis.europa.eu/project/id/INTAS-1999-01705/de

European Union, 2024