On an axiomatic approach to geometric prequantization: A classification scheme à la Kostant-Souriau-Kirillov

Journal of Mathematical Sciences

Volumn 95, Issue 6, 1999, Pages 2648-2668

  Mallios, A ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141692849     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/BF02169285     Document Type: Article

References (18)

1. R. J. Blattner, "On geometric quantization," In: Proc. of "Nonlinear Partial Differential Operators and Quantization Procedures," Clausthal 1981 (S. I. Andersson and H.-D. Doebner, eds.). Lect. Notes Math., Vol. 1037, Springer-Verlag, Berlin (1983), pp. 209-241.
2. N. Bourbaki, Algèbre I, Chap. 1-3, Hermann, Paris (1970).
3. M. Göckeler and T. Schücker, Differential Geometry, Gauge Theories, and Gravity, Cambridge Univ. Press, Cambridge (1987).
4. R. C. Gunning, Lectures on Riemann Surfaces, Princeton Univ. Press, Princeton, New Jersey (1967).
5. A. A. Kirillov, Elements of the Theory of Representations, Springer-Verlag, Berlin (1976).
6. A. A. Kirillov, "Geometric quantization," In: Dynamical Systems IV. Symplectic Geometry and Its Applications (V. I. Arnold and S. P. Novikov, eds.), Springer-Verlag, Berlin (1990), pp. 137-172.
7. A. Mallios, Topological Algebras, Selected Topics, North-Holland, Amsterdam (1986).
8. A. Mallios, "Continuous vector bundles over topological algebras, II," J. Math. Anal. Appl., 132, 401-423 (1988).
9. A. Mallios, "On an abstract form of Weil's integrality theorem," Note Mat., 12, 167-202 (1992).
10. A. Mallios, "On geometric topological algebras," J. Math. Anal. Appl., 172, 301-322 (1993).
11. A. Mallios, "The de Rham-Kähler complex of the Gel'fand sheaf of a topological algebra," J. Math. Anal. Appl., 175, 143-168 (1993).
12. A. Mallios, Geometry of Vector Sheaves. An Axiomatic Approach to Differential Geometry. Vol. I (Chaps. I-V), Vol. II (Chaps. VI-XI), to appear.
13. Yu. I. Manin, Gauge Field Theory and Complex Geometry, Springer-Verlag, Berlin (1988).
14. M. Postnikov, Lecons de Géométrie. Géométrie Différentielle, Mir, Moscow (1990).
15. M. Puta, Hamiltonian Mechanical Systems and Geometric Quantization, Kluwer, Dordrecht (1993).
16. J.-M. Souriau, Structure des Systèmes Dynamiques, Dunod, Paris (1970).
17. R. O. Wells, Differential Analysis on Complex Manifolds, Springer-Verlag, New York (1980).
18. N. Woodhouse, Geometric Quantization, Oxford Univ. Press, Oxford (1980).