QFT on fuzzy disc and Calogero–Moser phase space

Noncommutative spaces with boundaries are expected to play an important role in connection between Feynman and functorial definitions of quantum field theory. Since actions of all field theories may be written in terms of De Rham algebra, the crucial step is to construct it on such noncommutative spaces. Here, we do it for the fuzzy disc. In our construction, we had to include new degrees of freedom associated to boundary. Surprisingly, the noncommutative analogue of the moduli space of flat connections turns out to be a phase space of Calogero–Moser system. We proceed by construction of noncommutative analogue of the Chern–Simons theory for fuzzy disc. We found that the Chern–Simons matrix model of Polychronakos coincides with ours up to Hamiltonian (that our model does not have).