The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
Toeplitz quantization of Kähler manifolds anggl(N), N→∞ limits
Open accessAbstract
For general compact Kähler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a well-defined (by operator norm estimates) classical limit. This generalizes earlier results of teh authors and Klimek and Lesniewski obtained for the tours and higher genus Riemann surfaces, respectively. We thereby arrive at an approximation of the Poisson algebra by a sequence of finitedimensional matrix algebrasgl(N), N→∞.
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Cites
Mathematical Methods of Classical Mechanics
Arnold, V. I. (1989) · Graduate Texts in Mathematics · doi:10.1007/978-1-4757-2063-1 · Cited by 9,116
Principles of Algebraic Geometry
Griffiths, P., & Harris, J. (1994) · Wiley · doi:10.1002/9781118032527 · Cited by 6,765
The Analysis of Linear Partial Differential Operators I
Hörmander, L. (1998) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-642-96750-4 · Cited by 5,721
Mathematical Methods of Classical Mechanics
Arnold, V. I. (1978) · Graduate Texts in Mathematics · doi:10.1007/978-1-4757-1693-1 · Cited by 5,106
Hörmander, L. (1971) · Acta Mathematica · doi:10.1007/bf02392052 · Cited by 2,306
Deformation theory and quantization. I. Deformations of symplectic structures
Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., & Sternheimer, D. (1978) · Annals of Physics · doi:10.1016/0003-4916(78)90224-5 · Cited by 1,481
Invariance theory, the heat equation, and the Atiyah-Singer index theorem
Gilkey, P. (1995) · Cited by 1,469
Groups of Diffeomorphisms and the Motion of an Incompressible Fluid
Ebin, D. G., & Marsden, J. (1970) · The Annals of Mathematics · doi:10.2307/1970699 · Cited by 1,224
(2010) · Geometric Formulation of Classical and Quantum Mechanics · doi:10.1142/9789814313735_0006 · Cited by 1,108
Differential Analysis on Complex Manifolds
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Cited by
M(atrix) theory: matrix quantum mechanics as a fundamental theory
Taylor, W. (2001) · Reviews of Modern Physics · doi:10.1103/revmodphys.73.419 · Cited by 306
Introduction to M(atrix) theory and noncommutative geometry
Konechny, A., & Schwarz, A. (2002) · Physics Reports · doi:10.1016/s0370-1573(01)00096-5 · Cited by 254
Metadata
- Authors
- Bordemann, M., Meinrenken, E., & Schlichenmaier, M.
- Venue
- Communications in Mathematical Physics
- Published
- 1994-10
- Volume
- 165
- Issue
- 2
- Pages
- 281-296
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W1484902804
- Cited by
- 333
- References
- 21
- FWCI
- 7.72
- Type
- journal article
- Language
- en
- Open access
- green
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- Bordemann, M., Meinrenken, E., & Schlichenmaier, M. (1994). Toeplitz quantization of Kähler manifolds anggl(N), N→∞ limits. Communications in Mathematical Physics. https://doi.org/10.1007/bf02099772
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