Physical phase space of the lattice Yang--Mills theory and moduli space of flat connections on a Riemann surface
Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 1, pp. 100-111
Voir la notice de l'article provenant de la source Math-Net.Ru
It is shown that the physical phase space of $\gamma$-deformed, Hamiltonian-lattice Yang–Mills theory, which was recently proposed in [1], [2], 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, where $L$ and $V$ are, respectively, the total number of links and vertices of the lattice. The deformation parameter $\gamma$ is identified with $2\pi/k$ and $k$ is an integer entering the Chern–Simons action.
@article{TMF_1997_113_1_a8,
author = {S. A. Frolov},
title = {Physical phase space of the lattice {Yang--Mills} theory and moduli space of flat connections on a {Riemann} surface},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {100--111},
publisher = {mathdoc},
volume = {113},
number = {1},
year = {1997},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1997_113_1_a8/}
}
TY - JOUR AU - S. A. Frolov TI - Physical phase space of the lattice Yang--Mills theory and moduli space of flat connections on a Riemann surface JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1997 SP - 100 EP - 111 VL - 113 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1997_113_1_a8/ LA - ru ID - TMF_1997_113_1_a8 ER -
%0 Journal Article %A S. A. Frolov %T Physical phase space of the lattice Yang--Mills theory and moduli space of flat connections on a Riemann surface %J Teoretičeskaâ i matematičeskaâ fizika %D 1997 %P 100-111 %V 113 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1997_113_1_a8/ %G ru %F TMF_1997_113_1_a8
S. A. Frolov. Physical phase space of the lattice Yang--Mills theory and moduli space of flat connections on a Riemann surface. Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 1, pp. 100-111. http://geodesic.mathdoc.fr/item/TMF_1997_113_1_a8/