D Bar-Moshe and M S Marinov 1994 J. Phys. A: Math. Gen. 27 6287 doi:10.1088/0305-4470/27/18/035
D Bar-Moshe and M S Marinov
Show affiliationsThe Berezin quantization on a simply connected homogeneous Kahler manifold, which is considered as a phase space for a dynamical system, enables a description of the quantal system in a (finite-dimensional) Hilbert space of holomorphic functions corresponding to generalized coherent states. The Lie algebra associated with the manifold symmetry group is given in terms of first-order differential operators. In the classical theory, the Lie algebra is represented by the momentum maps which are functions on the manifold, and the Lie product is the Poisson bracket given by the Kahler structure. The Kahler potentials are constructed for the manifolds related to all compact semi-simple Lie groups. The complex coordinates are introduced by means of the Borel method. The Kahler structure is obtained explicitly for any unitary group representation. The cocycle functions for the Lie algebra and the Killing vector fields on the manifold are also obtained.
17Bxx Lie algebras and Lie superalgebras (For Lie groups, see 22Exx)
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
Issue 18 (21 September 1994)
D Bar-Moshe and M S Marinov 1994 J. Phys. A: Math. Gen. 27 6287
J. G. Kirk et al. 2000 ApJ 542 235
Hugo Nguyen et al 2006 J. Micromech. Microeng. 16 2369
X M Zhu et al 2009 J. Phys. D: Appl. Phys. 42 142003
John Paul Strachan et al 2009 Nanotechnology 20 485701
A Baram 1982 J. Phys. C: Solid State Phys. 15 2925
Nicholas P Warner 2001 Class. Quantum Grav. 18 3159
Heather E Findlay and Paula J Booth 2006 J. Phys.: Condens. Matter 18 S1281
A. Ptak and E. Colbert 2004 ApJ 606 291
Anjli Chhikara et al 1999 J. Phys.: Condens. Matter 11 L229