TY  - INPR
A1  - Fedosov, Boris
T1  - Non-Abelian reduction in deformation quantization
N2  - We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B. In other words, we show that the reduction commutes with the canonical G-invariant deformation quantization. A similar statement in the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now completely proved).
T3  - Preprint - (1997) 26 
KW  - deformation quantization
KW  - Hamiltonian group action
KW  - moment map
KW  - classical and quantum reduction
Y1  - 2008
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2306
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-25101
ER  -