@unpublished{Fedosov1998, author = {Fedosov, Boris}, title = {Moduli spaces and deformation quantization in infinite dimensions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25396}, year = {1998}, abstract = {We construct a deformation quantization on an infinite-dimensional symplectic space of regular connections on an SU(2)-bundle over a Riemannian surface of genus g ≥ 2. The construction is based on the normal form thoerem representing the space of connections as a fibration over a finite-dimensional moduli space of flat connections whose fibre is a cotangent bundle of the infinite-dimensional gauge group. We study the reduction with respect to the gauge groupe both for classical and quantum cases and show that our quantization commutes with reduction.}, language = {en} } @unpublished{Fedosov2006, author = {Fedosov, B.}, title = {On a spectral theorem for deformation quantization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30161}, year = {2006}, abstract = {We give a construction of an eigenstate for a non-critical level of the Hamiltonian function, and investigate the contribution of Morse critical points to the spectral decomposition. We compare the rigorous result with the series obtained by a perturbation theory. As an example the relation to the spectral asymptotics is discussed.}, language = {en} }