A remark on Berezin's quantization and cut locus

Reports on Mathematical Physics

Volumn 40, Issue 2, 1997, Pages 159-168

  Berceanu, Stefan ^a  

^a HORIA HULUBEI NATIONAL INSTITUTE OF PHYSICS AND NUCLEAR ENGINEERING   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031256740     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0034-4877(97)85912-5     Document Type: Article

References (41)

1. [1] S. Berceanu: Coherent states and global differential geometry, in Quantization, Coherent States, and Complex Structures, eds. J.-P. Antoine, S. Twareque Ali, W. Lisiecki, I. M. Mladenov and A. Odzijewicz, Plenum, New York 1995; S. Berceanu: J. Geom. Phys. 21 (1997), 149.
2. [1] S. Berceanu: Coherent states and global differential geometry, in Quantization, Coherent States, and Complex Structures, eds. J.-P. Antoine, S. Twareque Ali, W. Lisiecki, I. M. Mladenov and A. Odzijewicz, Plenum, New York 1995; S. Berceanu: J. Geom. Phys. 21 (1997), 149.
3. [2] J. R. Klauder and B. S. Skagerstam, eds.: Coherent States, Word Scientific, Singapore 1985.
4. [3] S. Berceanu: The coherent states: old geometrical methods in new quantum clothes, Bucharest preprint FT-398-1994, hep-th/9408008; S. Berceanu: Coherent states, embeddings and transition amplitudes, in Proceeding the XIV Workshop on Geometrical Methods in Physics, Bialowiez̀a, Poland, 9-15 July 1995, eds. S. Twareque Ali, A. Odzijewicz and A. Strasburger, to appear; S. Berceanu: Geometry via coherent states, in GROUP 21: Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras, eds. M.-D. Doebner, W. Scherer, P. Nattermann, World Scientific, Singapore 1997.
5. [3] S. Berceanu: The coherent states: old geometrical methods in new quantum clothes, Bucharest preprint FT-398-1994, hep-th/9408008; S. Berceanu: Coherent states, embeddings and transition amplitudes, in Proceeding the XIV Workshop on Geometrical Methods in Physics, Bialowiez̀a, Poland, 9-15 July 1995, eds. S. Twareque Ali, A. Odzijewicz and A. Strasburger, to appear; S. Berceanu: Geometry via coherent states, in GROUP 21: Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras, eds. M.-D. Doebner, W. Scherer, P. Nattermann, World Scientific, Singapore 1997.
6. [3] S. Berceanu: The coherent states: old geometrical methods in new quantum clothes, Bucharest preprint FT-398-1994, hep-th/9408008; S. Berceanu: Coherent states, embeddings and transition amplitudes, in Proceeding the XIV Workshop on Geometrical Methods in Physics, Bialowiez̀a, Poland, 9-15 July 1995, eds. S. Twareque Ali, A. Odzijewicz and A. Strasburger, to appear; S. Berceanu: Geometry via coherent states, in GROUP 21: Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras, eds. M.-D. Doebner, W. Scherer, P. Nattermann, World Scientific, Singapore 1997.
7. [4] J. H. Rawnsley: Quart J. Math. Oxford (2) 28 (1977), 403.
8. [5] V. Ceausescu and A. Gheorghe: Classical limit and quantization of Hamiltonian systems, in: Symmetries and Semiclassical Features of Nuclear Dynamics, ed. A. A. Raduta, Lecture Notes in Physics, Vol. 279, Springer, Berlin 1987.
9. [6] A. Odzijewicz: Commun. Math. Phys. 150 (1992), 385.
10. [7] B. Kostant: Quantization and Unitary Representations, in Lecture Notes in Mathematics, Vol. 170, ed. C. T. Taam, Springer, Berlin 1970.
11. [8] F. A. Berezin: Math. USSR. Izvestjia 8 (1975), 1109; F. A. Berezin: Math. USSR. Izvestjia 9 (1975), 341; F. A. Berezin: Commun. Math. Phys. 40 (1975), 153.
12. [8] F. A. Berezin: Math. USSR. Izvestjia 8 (1975), 1109; F. A. Berezin: Math. USSR. Izvestjia 9 (1975), 341; F. A. Berezin: Commun. Math. Phys. 40 (1975), 153.
13. [8] F. A. Berezin: Math. USSR. Izvestjia 8 (1975), 1109; F. A. Berezin: Math. USSR. Izvestjia 9 (1975), 341; F. A. Berezin: Commun. Math. Phys. 40 (1975), 153.
14. [9] E. Onofri: J. Math. Phys. 16 (1975), 1087.
15. [10] C. Moreno: Lett. Math. Phys. 12 (1986), 217.
16. [11] M. Cahen, S. Gutt and J. Rawnsley: J. Geom. Phys. 7 (1990), 45; Trans. Math. Soc. 337 (1993), 73; Lett. Math. Phys. 30 (1994), 291; Lett. Math. Phys. 34 (1995), 159.
17. [11] M. Cahen, S. Gutt and J. Rawnsley: J. Geom. Phys. 7 (1990), 45; Trans. Math. Soc. 337 (1993), 73; Lett. Math. Phys. 30 (1994), 291; Lett. Math. Phys. 34 (1995), 159.
18. [11] M. Cahen, S. Gutt and J. Rawnsley: J. Geom. Phys. 7 (1990), 45; Trans. Math. Soc. 337 (1993), 73; Lett. Math. Phys. 30 (1994), 291; Lett. Math. Phys. 34 (1995), 159.
19. [11] M. Cahen, S. Gutt and J. Rawnsley: J. Geom. Phys. 7 (1990), 45; Trans. Math. Soc. 337 (1993), 73; Lett. Math. Phys. 30 (1994), 291; Lett. Math. Phys. 34 (1995), 159.
20. [12] S. Berceanu and A. Gheorghe: J. Math. Phys. 28 (1987), 2899.
21. [13] S. Berceanu and L. Boutet de Monvel: J. Math. Phys. 34 (1993), 2353.
22. [14] P. Griffith and J. Harris: Principles of Algebraic Geometry, Wiley, New York 1978.
23. [15] S. Berceanu: Bull. Belgian Math. Soc. 4 (1997), 205.
24. [16] R. Bott: Ann. Math. 66 (1957), 203.
25. [17] J. A. Tirao and J. A. Wolf: Indiana Univ. Math. J. 20 (1970), 15.
26. -éme année, 1953/1959, Exp. 100, Paris, (1959), 2nd edition.
27. [19] J. A. Wolf: Bull. Am. Math. Soc. 75 (1969), 1121.
28. [20] B. Shiffman and A. J. Sommese: Vanishing Theorems on Complex Manifolds, Progress in Mathematics, Vol. 56, Birkhäuser, Boston 1985.
29. [21] D. Husemoller: Fibre Bundles, Mc Craw-Hill, New York 1966.
30. [22] A.M. Perelomov: Commun. Math. Phys. 26 (1972), 222.
31. [23] V. Bargmann: Ann. Math. 59 (1954), 1.
32. [24] E. P. Wigner: Group Theory and its Applications in Quantum Mechanics of Atomic Spectra, Academic Press, London 1959.
33. [25] G. Emch and C. Piron: J. Math. Phys. 4 (1963), 469.
34. [26] E. Artin: Geometric Algebra, Interscience Publishers, New York 1957.
35. [27] S. Berceanu: From quantum mechanics to classical mechanics and back, via coherent states, in Quantization and Infinite-Dimensional Systems, eds. J.-P. Antoine, S.T. Ali, W. Lisiecki, I. Mladenov and A. Odzijewicz, Plenum, New York 1994.
36. [28] Z. Pasternak-Winiarski: On reproducing kernels for holomorphic vector bundles, in Quantization and Infinite-Dimensional Systems, eds. J.-P. Antoine, S. T. Ali, W. Lisiecki, I. Mladenov and A. Odzijewicz, Plenum, New York 1994.
37. [29] S. Kobayashi and K. Nomizu: Foundations of Differential Geometry, Vol. II, Interscience, New York 1969.
38. [30] H.H. Wu: The Equidistribution Theory of Holomorphic Curves, Annals of Maths. Studies 164, Princeton University Press, Princeton 1970.
39. [31] E. Calabi: Ann. Math. 58 (1953), 1.
40. [32] M. Schlichenmaier: private communication.
41. [33] S. Berceanu: On the geometry of coherent states, in preparation.