Physical phase space of the lattice Yang-Mills theory and the moduli space of flat connections on a riemann surface |
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Authors: | S A Frolov |
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Institution: | (1) Physics Section, Munich University, Theresienstr. 37, 80333 Munich, Germany;(2) Present address: Steklov Mathematical Institute, Vavilov st. 42, GSP-1, 117966 Moscow, Russia |
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Abstract: | It is shown that the physical phase space of the γ-deformed Hamiltonian lattice in the Yang-Mills theory coincides as a Poisson
manifold with the moduli space of flat connections on a Riemann surface with L−V+1 handles and, therefore, with the physical
phase space of the corresponding (2+1)-dimensional Chern-Simons model. Here, L and V are, respectively, the total number of
links and vertices of the lattice. The deformation parameter γ is identified with 2π/k, where k is an integer appearing in
the Chern-Simons action.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 100–111, October, 1997. |
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