Non-Abelian Reduction in Deformation Quantization

Letters in Mathematical Physics

Volumn 43, Issue 2, 1998, Pages 137-154

  Fedosov, Boris V ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Classical and quantum reduction; Deformation quantization; Hamiltonian group action; Moment map

Indexed keywords

EID: 0002211268     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007451214380     Document Type: Article

References (10)

1. Marsden, J. E. and Weinstein, A.: Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5 (1974), 121-130.
2. Fedosov, B. V.: A simple geometrical construction of deformation quantization, J. Differential Geom. 40 (1994), 213-238.
3. Fedosov B. V.: Deformation Quantization and Index Theory, Akademie Verlag, Berlin, 1996.
4. Gotay, M. J.: On coisotropic embeddings of presymplectic manifolds, Proc. Amer. Math. Soc. 84 (1982), 111-114.
5. Astashkevich, A.: Fedosov's quantization of the coadjoint orbits, Thesis, Massachusetts Institute of Technology, 1996.
6. Guillemin, V. and Sternberg, S.: Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1981), 513-538.
7. Meinrenken, E.: On Riemann-Roch formulas for multiplicities, J. Amer. Math. Soc. 9 (1996), 373-389.
8. Vergne, M.: Multiplicity formula for geometric quantization. I,II, Duke Math. J. 82 (1996), 143-194.
9. Bayen, F., Flato, M., Fronsdal, C., Lichnerowitz, A. and Sternheimer, D.: Deformation theory and quantization. I, II, Ann. Phys. 111 (1978), 61-151.
10. Gutt, S.: An explicit *-product on the cotangent bundle of a Lie group, Lett. Math. Phys. 7 (1983), 249-258.