Non-Abelian reductions in deformation quantization

作     者：Fedosov, BV 

作者机构：Univ Potsdam Inst Math D-14415 Potsdam Germany 

出 版 物：《LETTERS IN MATHEMATICAL PHYSICS》 (数理物理学快报)

年 卷 期：1998年第43卷第2期

页      面：137-154页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

主　　题：deformation quantization Hamiltonian group action moment map classical and quantum reduction 

摘      要：We consider a G-invariant star-product algebra (A) over cap on a symplectic manifold (M,omega) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein Theorem we define a reduction of the algebra (A) over cap 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 within the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now, completely proved).