Quantization methods: A guide for physicists and analysts

Reviews in Mathematical Physics

Volumn 17, Issue 4, 2005, Pages 391-490

  Ali, S Twareque ^a   Engliš, Miroslav ^b  

^a Gina Cody School of Engineering and Computer Science   (Canada)

^b MÚ AV ČR ^*  (Czech Republic)

Author keywords

Berezin quantization; Bereziu Touplitz quantization; Borel quantization; Canonical quantization; Coherent state quantization; Deformation quantization; Geometric quantization

Indexed keywords

EID: 21344470147     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X05002376     Document Type: Review

References (342)

1. Y. Aharonov and D. Bohm. Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115 (1959) 485-491.
2. S. Albeverio arid A. Yu. Daletskii, Asymptotic quantization for solution manifolds of some infinite-dimensional Hamiltonian systems. J. Geom. Phys. 19 (1996) 31-46.
3. S. T. Ali, Survey of quantization methods, in Classical and Quantum Systems (Goslar 1991) (World Scientific River Edge. NJ 1993), pp. 29-37.
4. S. T. Ali, Coherent states and quantization, in Spline Functions and the Theory of Wavelets (Montreal, PQ, 1996) CRM Proc. Lecture Notes, Vol. 18 (AMS, Providence, 1999), pp. 233-243.
5. S. T. Ali, Quantization techniques: A quick overview, in Contemporary Problems in Mathematical Physics (World Scientific, Singapore. 2002), pp. 3-78.
6. S. T. Ali and J.-P. Antoine, Quantum frames, quantization and dequantization, Quantization and Infinite-Dimensional Systems (Plenum, New York, 1994), pp. 133-145.
7. S. T. Ali, J.-P. Antoine, J.-P. Gazeau and U. A. Mueller, Coherent states and their generalizations: A mathematical overview, Rev. Math. Phys. 7 (1995) 1013-1104.
8. S. T. Ali, J.-P. Antoine and J.-P. Gazeau, Coherent States, Wavelets, and Their Generalizations (Springer, Berlin-Heidelberg-New York, 2000).
9. S. T. Ali and H.-D. Doebner, Ordering problem in quantum mechanics: Prime quantization and its physical interpretation, Phys. Rev. A41 (1990) 1199-1210.
10. S. T. Ali and G. G. Emch, Geometric quantization: Modular reduction theory and coherent states, J. Math. Phys. 27 (1986) 2936-2943.
11. S. T. Ali, G. G. Emch and A. M. El-Gradechi, Modular algebras in geometric quantization, J. Math. Phys. 35 (1994) 6237-6243.
12. S. T. Ali and G. A. Goldin, Quantization, coherent states and diffeomorphism groups, in Differential Geometry, Group Representations, and Quantization, Lecture Notes in Phys., Vol. 379 (Springer, Berlin, 1991), pp. 147-178.
13. S. T. Ali and U. A. Mueller, Quantization of a classical system on a coadjoint orbit of the Poincaré group in 1 + 1 dimensions, J. Math. Phys. 35 (1994) 4405-4422.
14. S. T. Ali and E. Prugovečki, Mathematical problems of stochastic quantum mechanics: Harmonic analysis on phase space and quantum geometry, Acta Appl. Math. 6 (1986) 1-18;
15. Extended harmonic analysis of phase space representations for the Galilei group, Acta Appl. Math. 6 (1986) 19-45;
16. Harmonic analysis and systems of covariance for phase space representations of the Poincaré group, Acta Appl. Math. 6 (1986) 47-62.
17. R. F. V. Anderson, The Weyl functional calculus, J. Fund. Anal. 4 (1969) 240-267;
18. On the Weyl functional calculus, J. Fund. Anal. 6 (1970) 110-115;
19. The multiplicative Weyl functional calculus, J. Fund. Anal. 9 (1972) 423-440.
20. B. Angermann, Über quantisierungen lokalisierbarer systeme - physikalisch interpretierbare mathematische modelle, Dissertation, Technische Universität Clausthal, 1983.
21. B. Angermann, H.-D. Doebner and J. Tolar, Quantum kinematics on smooth manifolds, in Nonlinear Partial Differential Operators and Quantization Procedure it (Springer Berlin-Heidelberg-New York, 1983), pp. 171-208.
22. J. Arazy and H. Upmeier, Invariant symbolic calculi and eigenvalues of invariant operators on symmetric domains, Function Spaces, Interpolation Theory, and Related Topics (Lund, 2000), eds. A. Kufner, M. Cwikel, M. Engliš, L.-E. Persson and G. Sparr (Walter de Gruyter, Berlin, 2002), pp. 151-211.
23. R. Arens and D. Babbitt, Algebraic difficulties of preserving dynamical relations when forming quantum-mechanical operators, J. Math. Phys. 6 (1965) 1071-1075.
24. D. Arnal, M. Cahen and S. Gutt, Representation of compact Lie groups and quantization by deformation, Acad. Roy. Belg. Bull. Cl Sci. 74(5) (1988) 123-141.
25. D. Arnal, J. C. Cortet, M. Flato and D. Sternheimer, Star-products: Quantization and representation without operators, in Field Theory, Quantization and Statistical Physics, D. Reidel (1981), pp. 85-111.
26. A. Ashtekar, Asymptotic quantization Monographs and textbooks in physical science. Lecture notes, Vol. 2 (Bibliopolis, Naples, 1987); New perspectives in canonical gravity (Bibliopolis, Naples, 1988).
27. P. Bandyopadhyay, Geometry, Topology and Quantization, Mathematics and its Applications, Vol. 386 (Kluwer, Dordrecht, 1996).
28. D. H. Bao and Z. Y. Zhu, Ordering problem in geometric quantization, J. Phys. A25 (1992) 2381-2385.
29. D. H. Bao and Z. Y. Zhu, Operator ordering problem and coordinate-free nature of geometric quantization, Comm. Theor. Phys. 25 (1996) 189-194.
30. D. Bar-Moshe and M. S. Marinov, Realization of compact Lie algebras in Kähler manifolds, J. Phys. A27 (1994) 6287-6298.
31. A. Barnard and R. E. Borcherds, Quantum field theory, preprint math-ph/0204014.
32. I. A. Batalin, E. S. Pradkin and T. E. Fradkina, Another version for operatorial quantization of dynamical systems with irreducible constraints, Nuclear Phys. B314 (1989) 158 174; Erratum ibid. 323 (1989) 734-735;
33. Generalized canonical quantization of dynamical systems with constraints and curved phase space, Nuclear Phys. B332 (1990) 723-736.
34. I. A. Batalin and I. V. Tyutin, Quantum geometry of symbols and operators, Nuclear Phys. B345 (1990) 645-658.
35. S. Bates and A. Weinstein, Lectures on the Geometry of Quantization, Berkeley Mathematics Lecture Notes, Vol. 8 (Amer. Math. Soc., Providence, 1997).
36. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization, Lett. Math. Phys. 1 (1977) 521-530;
37. Ann. Phys. 111 (1978) 61-110 (Part I), 111-151 (Part II).
38. S. Berceanu, Coherent states and geodesies: Cut locus and conjugate locus, J. Geom. Phys. 21 (1997) 149-168;
39. A remark on Berezin's quantization and cut locus, in Quantizations, Deformations and Coherent States, Bialowieza, 1996, Rep. Math. Phys. 40 (1997) 159-168.
40. F. A. Berezin, Quantization, Math. USSR Izvestiya 8 (1974) 1109-1163;
41. Quantization in complex symmetric spaces, Math. USSR Izvestiya 9 (1975) 341-379;
42. General concept of quantization, Commun. Math. Phys. 40 (1975) 153-174.
43. F. A. Berezin, The Method of Second Quantization, 2nd edn. (Nauka, Moscow, 1986) (in Russian).
44. F. A. Berezin and M. A. Shubin, The Schrödinger Equation Moscow, 1983; English translation (Kluwer, Dordrecht, 1991).
45. M. Bertelson, M. Cahen and S. Gutt, Equivalence of star products, Class. Quant. Grav. 14 (1997) A93-A107.
46. R. J. Blattner, Quantization and representation theory, Harmonic analysis on homo geneous spaces, Williamstown, 1972, in Proc. Symp. Pure Math., Vol. XXVI (Amer. Math. Soc., Providence, 1973), pp. 147-165.
47. R. J. Blattner, Pairing of half-form spaces, Géométrie symplectique et physique mathématique, Aix-en-Provence, 1974 (CNRS, Paris, 1975), pp. 175-186.
48. R. J. Blattner, The metalinear geometry of non-real polarizations, Differential Geometrical Methods in Mathematical Physics (Bonn, 1975) Lecture Notes in Math., Vol. 570 (Springer, Berlin, 1977), pp. 11-45.
49. R. J. Blattner, Some remarks on quantization, Symplectic Geometry and Mathematical Physics (Aix-en-Provence, 1990) Progr. Math. Vol. 99 (Birkhäuser, Boston, 1991), pp. 37-47.
50. 2(k+l) J. Funct. Anal. 50 (1983) 188-214.
51. R. J. Blattner and J. H. Rawnsley, A cohomological construction of half-forms for nonpositive polarizations, Bull. Soc. Math. Belg. Sér. B 38 (1986) 109-130.
52. B. G. Bodmann, Construction of self-adjoint, Berezin-Toeplitz operators on Kähler manifolds and a probabilistic representation of the associated semigroups, preprint math-ph/0207026.
53. J. -M. Bony and N. Lerner, Quantification asymptotique et microlocalisations d'ordre superieur, in Séminaire sur les equations aux dérivées partielles 1986-1987. Exp. No. 11-111 (Éolo Polytech., Palaiseau, 1987);
54. Ann. Sci. École Norm. Sup. 22(4) (1989) 377-433.
55. n, Lett. Math. Phys. 36 (1996) 357-371;
56. n, J. Math. Phys. 37 (1996) 6311-6323.
57. M. Bordemann, H.-C. Herbig and S. Waldmann, ERST cohornology and phase space reduction in deformation quantization, Commun. Math. Phys. 210 (2000) 107-144.
58. M. Bordemann, E. Meinrenken and M. Schlichenmaier, Toeplitz quantization of Kähler manifolds and gl(N), N → ∞ limits, Commun. Math. Phys. 165 (1994) 281-296.
59. M. Bordemann and S. Waldmann, A Fedosov star product of Wick type for Kähler manifolds, Lett. Math. Phys. 41 (1997) 243-253.
60. D. Borthwick, Microlocal techniques for semiclassical problems in geometric quantization, in Perspectives on Quantization (South Hadley, MA, 1996), pp. 23-37, Contemp. Math. Vol. 214 (AMS, Providence, 1998).
61. D. Borthwick, Introduction to Kähler quantization, First Summer School in Analysis and Mathematical Physics (Cuernavaca Morelos, 1998), Contemp. Math. 260 (Amer. Math. Soc. Providence 2000), pp. 91-132.
62. D. Borthwick, A. Lesniewski and H. Upmeier, Nonperturbative deformation quantization of Cartan domains, J. Fund. Anal. 113 (1993) 153-176.
63. D. Borthwick, S. Klimek, A. Lesniewski and M. Rinaldi, Matrix Cartan super-domains, super Toeplitz operators, and quantization, J. Fund. Anal. 127 (1995) 456-510.
64. D. Borthwick and A. Uribe, Almost complex structures and geometric quantization, Math. Res. Lett. 3 (1996) 845-861.
65. L. Boutet de Monvel, Toeplitz operators - an asymptotic quantization of symplectic cones, Stochastic processes and their applications in mathematics and physics (Bielefeld, 1985), Math. Appl. Vol. 61 (Kluwer, Dordrecht, 1990), pp. 95-106.
66. L. Boutet de Monvel and V. Guillemin, The Spectral Theory of Toeplitz Operators, Ann. Math. Studies, Vol. 99 (Princeton University Press, Princeton, 1981).
67. O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vol. I (Springer-Verlag, New York-Berlin-Heidelberg, 1979).
68. M. Braverman, Index theorem for equivariant Dirac operators on non-compact manifolds, math-ph/0011045.
69. M. Cahen, Déformations et quantification, Physique quantique et géométrie (Paris, 1986) Travaux en Cours, Vol. 32 (Hermann, Paris, 1988), pp. 43-02.
70. M. Cahen, S. Gutt and J. Rawnsley, Quantization of Kähler manifolds. I: Geometric interpretation of Berezin's quantization, J. Geom. Physics 7 (1990) 45-62;
71. Quantization of Kähler manifolds. II: Geometric interpretation of Berezin's quantization, Trans. Amer. Math. Soc. 337 (1993) 73-98;
72. Quantization of Kähler manifolds. III: Geometric interpretation of Berezin's quantization, Lett. Math. Phys. 30 (1994) 291-305;
73. Quantization of Kähler manifolds. IV: Geometric interpretation of Berezin's quantization, Lett. Math. Phys. 34 (1995) 159-168.
74. E. Calabi, Isometric imbedding of complex manifolds, Ann. Math. 58 (1953) 1-23.
75. A. Cannas da Silva and A. Weinstein, Geometric Models for Noncommulative Algebras, Berkeley Mathematics Lecture Notes, Vol. 10, AMS, Providence; Berkeley Center for Pure and Applied Mathematics, Berkeley, 1999.
76. D. Catlin, The Bergman kernel and a theorem of Tian. in Analysis and Geometry in Several Complex Variables (Katata, 1997), Trends in Math. (Birkhauser, Boston, 1999), pp. 1-23.
77. A. S. Cattaneo and G. Felder, A path integral approach to the Kontsevich quantization formula, Commun. Math. Phys. 212 (2000) 591-611, preprint math.QA/9902090.
78. L. Charles, Feynman path integral and Toeplitz quantization, Helv. Phys. Acta 72 (1999) 341-355;
79. Berezin-Toeplitz operators, a semi-classical approach, Commun. Math. Phys. 239 (2003) 1-28;
80. Quasimodes and Bohr-Sommerfeld conditions for the Toeplitz operators, Comm. Partial Diff. Eqs. 28 (2003) 1527-1566.
81. S. Chaturvedi, A. K. Kapoor arid V. Srinivasan, Stochastic quantization scheme of Parisi and Wu, Monographs and Textbooks in Physical Science. Lecture Notes, Vol. 16 (Bibliopolis, Naples, 1990).
82. L. A. Coburn, Deformation estimates for the Berezin-Toeplitz quantization, Commun. Math. Phys. 149 (1992) 415-424;
83. Berezin-Toeplitz quantization, in Algebraic Methods in Operator Theory (Birklwuser, Boston, 1994), pp. 101-108.
84. A. Connes, Noncommulative Geometry (Academic Press, San Diego, 1994).
85. A. Connes and M. Flato, Closed star products and cyclic cohomology, Lett. Math. Phys. 24 (1992) 1-12;
86. A. Connes, M. Flato and D. Sternheimer, Closedness of star products and cohomologies, Lie Theory and Geometry, Progr. Math., Vol. 123 (Birkhäuser, Boston, 1994), pp. 241-259.
87. A. Connes and N. Higson, Almost homomorphisms and KK-theory, unpublished manuscript, available at http://math.psu.edu/higson/Papers/CH1.pdf, 1989.
88. L. Cornalba and W. Taylor IV, Holomorphic curves from matrices, Nuclear Phys. B536 (1999) 513-552, preprint hep-th/9807060.
89. J. Czyz, On geometric quantization and its connections with the Maslov theory, Rep. Math. Phys. 15 (1979) 57-97;
90. On geometric quantization of compact, complex manifolds, Rep. Math. Phys. 19 (1984) 167-178.
91. P. H. Damgaard and H. Hüffel, Stochastic quantization Phys. Rep. 152 (1987) 227-398.
92. R. Dashen and D. H. Sharp, Currents as coordinates for hadrons, Phys. Rev. 165 (1968) 1857-1866.
93. M. Davidson, G. Olafsson and G. Zhang, Laplace and Segal-Bargmann transforms on Hermitian symmetric spaces and orthogonal polynomials, J. Fund. Anal. 204 (2003) 157-195; Segal-Bargmann transform on Hermitian symmetric spaces and orthogonal polynomials, preprint math.RT/0206275;
94. M. Davidson and G. Olafsson, The generalized Segal-Bargmann transform and special functions, preprint math.RT/0307343.
95. P. Dazord and G. Patissier, La premiére classe de Chern comme obstruction a la quantification asymptotique, in Symplectic. Geometry, Groupoids, and Integrable Systems, Berkeley, CA, 1989. Math. Sci. Res. Inst. Publ., Vol. 20 (Springer, New York, 1991), pp. 73-97.
96. P. Deligne, Déformations de l'algèbre des fonctions d'une variété symplectique: Comparaison entre Fedosov et Dewilde, Lecomte, Sel. Math. 1(4) (1995) 667-697.
97. M. Dewilde and P. B. A. Lecomte, Existence of star products and of formal deformations of the Poisson Lie algebra of arbitrary symtplectic manifolds, Lett. Math. Phys. 7 (1983) 487-496.
98. P. A. M. Dirac, The Principles of Quantum Mechanics, 3rd edn. (Oxford, London, 1947).
99. G. Dito and D. Sternheimer, Deformation quantization: genesis, developments, and metamorphoses, in Proceedings of the Meeting between Mathematicians and Theoretical Physicists (Strasbourg, 2001), IRMA Lectures in Math. Theoret. Phys., Vol. 1 (Walter de Gruyter Berlin, 2002), pp. 9 54, preprint math.QA/0201168.
100. H. D. Doebner, P. Št'ovíček and J. Tolar, Quantization of kinematics on configuration manifolds, Rev. Math. Phys. 13 (2001) 1-47, preprint math-ph/0104013.
101. H.-D. Doebner P. Nattermann, Borel quantization: Kinematics and dynamics, Acta Phys. Polon. B27 (1996) 2327-2339.
102. C. Duval, A. M. El Gradechi and V. Ovsienko, Projectively and conformally invariant star-products, preprint math.QA/0301052.
103. A. Echeverria-Enriquez, M. C. Muñoz-Leconda, N. Roman-Roy and C. Victoria-Monge, Mathematical foundations of geometric quantization, Extracta Math. 13 (1998) 135-238.
104. M. Engliš and J. Peetre, On the correspondence principle for the quantized annulus, Math. Scand. 78 (1996) 183-206.
105. M. Engliš, Asymptotics of the Berezin transform and quantization on planar domains, Duke Math. J. 79 (1995) 57-76.
106. M. Engliš, Berezin quantization and reproducing kernels on complex domains, Trans. Amer. Math. Soc. 348 (1996) 411-479.
107. M. Engliš, A Forelli-Rudin construction and asymptotics of weighted Bergman kernels, J. Funct. Anal. 177 (2000) 257-281.
108. M. Engliš, Bergman kernels in analysis, operator theory and mathematical physics, Habilitation (DrSc.) thesis Prague, October 2000.
109. M. Engliš, Weighted Bergman kernels and quantization, Commun. Math. Phys. 227 (2002) 211-241.
110. M. Engliš, A no-go theorem for nonlinear canonical quantization, Commun. Theor. Phys. 37 (2002) 287-288.
111. M. Engliš, Berezin-Toeplitz quantization and invariant symbolic calculi, Lett. Math. Phys. 65 (2003) 59-74.
112. B. V. Fedosov, Deformation quantization and asymptotic operator representation, Funct. Anal. Appl. 25 (1991) 184-194.
113. B. V. Fedosov, A simple geometric construction of deformation quantization, J. Diff. Geo. 40 (1994) 213-238.
114. B. V. Fedosov, Deformation Quantization and Index Theory, Mathematical Topics, Vol. 9 (Akademie Verlag, Berlin 1996).
115. B. V. Fedosov, Deformation quantization: Pro and contra, in Quantization, Poisson Brackets and Beyond (Manchester, 2001), ed. T. Voronov, Contemp. Math. 315. (Amer. Math. Soc. Providence, 2002).
116. R. L. Fernandes, Deformation quantization and Poisson geometry, Resenhas IME-USP 4 (2000) 325-359.
117. R. P. Feynman and A. R. Hibbs, Quanium Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
118. R. Fioresi and M. A. Lledo, A review on deformation quantization of coadjoint orbits of semisimple Lie groups, preprint math.QA/0111132.
119. M. Flato und D. Sternheimer, Closedness of star products and cohomologies, in Lie Theory and Geometry, in Honor of B. Kostant, eds. J.-L. Brylinski, R. Brylinski, V. Guillemin and V. Kac (Birkhauser, Boston, 1994).
120. G. B. Folland, Harmonic Analysis in Phase Space, Annals of Mathematics Studies, Vol. 122 (Princeton University Press, Princeton, 1989).
121. E. S. Fradkin, Towards a quantum field theory in curved phase space, in Proceedings of the Second International A.D. Sakhamv Conference on Physics, Moscow. 1996 (World Scientific, River Edge, 1997), pp. 746-756.
122. E. S. Fradkin and V. Ya. Linetsky, BFV approach to geometric quantization, Nuclear Phys. B431 (1994) 569-621;
123. BFV quantization on Hermitian symmetric spaces, Nuclear Phys. B444 (1995) 577-601.
124. K. Gawȩdzki, On extensions of Kostant quantization procedure, Géométrie symplectique et physique mathématique (Aix-en-Provence, 1974), pp. 211-216, CNRS Paris, 1975.
125. K. Gawȩdzki, Fourier-like kernels in geometric quantization, Dissertationes Math. 128 (1976).
126. K. Gawȩdzki, Geometric quantization and Feynman path integrals for spin, in Differential Geometric Methods in Mathematical Physics (Proc. Sympos., Univ. Bonn, Bonn, 1975), Lecture Notes in Math., Vol. 570 (Springer, Berlin, 1977), pp. 67-71.
127. J.-P. Gazeau, Coherent states and quantization of the particle motion on the line, on the circle, on 1 + 1-de Sitter space-time and of more general systems, in Proceedings of the Third International Workshop on Contemporary Problems in Mathematical Physics (Cotonou 2003), eds. J. Govaerts, M. N. Hounkonnou and A. Z. Msezane (World Scientific, Singapore, 2005), pp. 465-479.
128. J.-P. Gazeau and W. Piechocki, Asymptotic coherent states quantization of a particle in de Sitter space, preprint hep-th/0308019 v1 4 Aug 2003.
129. M. Gerstenhaber, On deformations of rings and algebras, Ann. Math. 79 (1964) 59-103.
130. F. Gieres, Mathematical surprises and Dirac's formalism in quantum mechanics, Rep. Prog. Phys. 63 (2000) 1893-1946, preprint quant-ph/9907069.
131. R. J. Glauber, Coherent and incoherent states of the radiation field, Phys. Rev. 131(2) (1963) 2766-2788.
132. J. Glimm and A. Jaffe, Quantum Physics. A Functional Integral Point of View (Springer-Verlag, New York-Berlin, 1987).
133. G. A. Goldin, Non-relativistic current algebras as unitary representations of groups, J. Math. Phys. 12 (1971) 462-487.
134. G. A. Goldin, Lectures on diffeomorphism groups in quantum physics, in Proceedings of the Third International Workshop on Contemporary Problems in Mathematical Physics (Cotonou 2003), eds. J. Govaerts, M. N. Hounkonnou and A. Z. Msezane (World Scientific, Singapore, 2005), pp. 3-93.
135. G. A. Goldin, J. Grodnik, R. T. Powers and D. H. Sharp, Nonrelativistic current algebra in the 'N/V' limit. J. Math. Phys. 15 (1974) 88-100.
136. G. A. Goldin, R. Menikoff and D. H. Sharp, Particle statistics from induced representations of a local current group, J. Math. Phys. 21 (1980) 650-664.
137. G. A. Goldin, R. Menikoff and D. H. Sharp, Representations of a local current algebra in non-simply connected space and the Aharoriov-Bohm effect, J. Math. Phys. 22 (1981) 1664-1668.
138. G. A. Goldin, R. Menikoff and D. H. Sharp, Diffeomorphism groups, gauge groups and quantum theory, Phys. Rev. Lett. 51 (1983) 2246-2249.
139. 3n, J. Phys. A: Math. Gen. 16 (1983) 1827-1833.
140. G. A. Goldin and D. H. Sharp, Diffeomorphisin groups, anyon fields and q-commutators, Phys. Rev. Lett. 76 (1996) 1183-1187.
141. G. A. Goldin and D. H. Sharp, Lie algebras of local currents and their representations, in Group Representations in Mathematics and Physics: Battelle-Seattle 1969 Rencontres. Lecture Notes in Phys., Vol. 6 (Springer Berlin, 1970), pp. 300-310.
142. M. J. Gotay, A class of nonpolarizable symplectic manifolds, Monatsh. Math. 103 (1987) 27-30.
143. M. J. Gutay, H. B. Grundling and G. M. Tuynman, Obstruction results in quantization theory. J. Nonlinear, Sci. 6 (1996) 469-498.
144. J. M. Gracia-Bondia, Generalized Moyal quantization on homogeneous symplectic spaces, in Deformation Theory and Quantum Groups with Applications to Mathematical Physics, Amherst, MA, 1990, Contemp. Math., Vol. 134 (AMS, Providence, 1992), pp. 93-114.
145. R. M. Gray and D. L. Neuhoff, Quantization, IEEE Trans. Inform. Theory 44 (1998) 2325-2383.
146. W. Greiner and J. Reinhardt, Field Quantization (Springer-Verlag, Berlin, 1996).
147. M. A. Grigoriev and S. L. Lyakhovich, Fedosov quantization as a BRST theory, Commun. Math. Phys. 218 (2001) 437-457, preprint hep-th/0003114.
148. H. J. Groenewold, On the principles of elementary quantum mechanics, Physica 12 (1946) 405-460.
149. C. Grosche, An introduction into the Feynman path integral, preprint hep-th/9302097;
150. C. Grosche and F. Steiner, Handbook of Feynman Path Integrals, Springer Tracts in Modern Physics 145 (Springer-Verlag, Berlin, 1998).
151. E. Guentner, Berezin quantization and K-homology, Commun. Math. Phys. 240 (2003) 423-446;
152. Wick quantization and asymptotic morphisms, Houston J. Math. 26 (2000) 361-375.
153. V. Guillemin, Reduced phase spaces and Riemann-Roch, in Lie Theory and Geometry in Honour of B. Kostant, Progress in Math. 123 (Birkhäuser, Boston, 1994) pp. 304-334.
154. V. Guillemin, Star products on pre-quantizable symplectic manifolds, Lett. Math. Phys. 35 (1995) 85-89.
155. V. Guillemin, V. Ginzburg and Y. Karshon, Moment Maps, Cobordisms, and Hamiltonian Group Actions (Amer. Math. Soc., Providence, 2002).
156. V. Guillemin and S. Sternberg, Geometric Asymptotics, Math. Surveys, Vol. 14 (AMS, Providence, 1977).
157. V. Guillemin and S. Sternberg, Symplectic Techniques in Physics (Cambridge University Press, Cambridge, 1984).
158. S. Gutt, Variations on Deformation Quantization, Conférence Moshé Flato, Dijon, 1999, Vol. 1, Math. Phys. Stud. 21 (Kluwer, Dordrecht, 2000), pp. 217-254, preprint math.QA/0003107.
159. R. Haag, N. Hugenholtz and M. Winnink, On the equilibrium states in quantum statistical mechanics. Commun. Math. Phy. 5 (1967) 215-236.
160. K. Hajra and P. Bandyopadhyay, Equivalence of stochastic. Klauder and geometric quantization, Int. J. Mod. Phys. A7 (1992) 1267-1285.
161. E. Hawkins, The correspondence between geometric quantization and formal deformation quantization, preprint math/9811049 (1998).
162. H. Hess, On a geometric quantization scheme generalizing those of Kostant-Souriau and Czyz. in Differential Geometric Methods in Mathematical Physics, Clausthal-Zellerfeld, 1978, Lecture Notes in Phys., Vol. 139 (Springer, Berlin-New York, 1981), pp. 1-35.
163. L. Hörmander The Weyl calculus of pseudodifferential operators, Comm. Pure. Appl. Math. 32 (1979), 359-443.
164. n. Rep. Math. Phys. 24 (1986) 351-363.
165. L. van Hove, Sur certaines représentations unitaires d'un groupe infini de transformations, Mem. Acad. Roy. de Belgique, Classe den Sci. 26(6) (1951).
166. J. Huebschmann, Kähler quantization and reduction, preprint math/0207166.
167. N. E. Hurt, Geometric Quantization in Action (Dordrecht, Reidel, 1983).
168. L. A. Ibort, On the geometrical and cohomological foundations of BRST quantization, in Quantization of Constrained Systems and Conformal Field Theory, eds. J. F. Cariñena, G.I.F.T. (Zaragoza, 1990), pp. 201-255.
169. G. P. Jorjadze, Hamiltonian reduction and quantization on symplectic manifolds, Mem. Diff. Egs. Math. Phys. 13 (1998) 1-98.
170. A. V. Karabegov, Deformation quantization with separation of variables on a Kähler manifold, Commun. Math. Phys. 180 (1996) 745-755.
171. A. V. Karabegov, On deformation quantization on a Kählerian manifold that is related to the Berezin quantization, Funktsional. Anal. i Prilozhen. 30 (1996) 87-89;
172. Funct. Anal. Appl. 30 (1996) 142-144.
173. A. V. Karabegov, Berezin's quantization on flag manifolds and spherical modules, Trans. Amer. Math. Soc. 350 (1998) 1467-1479.
174. A. V. Karabegov, Cohomological classification of deformation quantizations with separation of variables, Lett. Math. Phys. 43 (1998) 347-357.
175. A. V. Karabegov, On the canonical normalization of a trace density of deformation quantization, Lett. Math. Phys. 45 (1998) 217-228.
176. A. V. Karabegov, Pseudo-Kähler quantization on flag manifolds, Commun. Math. Phys. 200 (1999) 355-379.
177. A. V. Karabegov and M. Schlichenmaier, Identification of Berezin-Toeplitz deformation quantization, J. Reine Angew. Math. 540 (2001) 49-76, preprint math.QA/0006063.
178. M. V. Karasev, Quantization by means of two-dimensional surfaces (membranes): Geometrical formulas for wave-functions, in Symplectic Geometry and Quantization Sanda and Yokohama, 1993, Contemp. Math. Vol. 179 (AMS, Providence, 1994) pp. 83-113,
179. Geometric star-products, ibid., pp. 115-121;
180. Geometric coherent states, membranes, and star products, in Quantization, Coherent States, and Complex Structures, Bialowieza, 1994 (Plenum, New York, 1995), pp. 185-199;
181. Quantization and coherent states over Lagrangian submanifolds, Russian J. Math. Phys. 3 (1995) 393-400.
182. M. V. Karasev, Simple quantization formula, in Symplectic Geometry and Mathematical Physics, Aix-en-Provencc, 1990, Progr. Math., Vol. 99 (Birkhäuser, Boston, 1991), pp. 234-244.
183. M. V. Karasev and V. P. Maslov, Asymptotic and geometric quantization, Uspekhi Mat. Nauk 39 (1984) 115-173;
184. Russian Math. Surveys 39 (1985) 133-205;
185. Pseudodifferential operators and the canonical operator on general symplectic manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 47 (1983) 999-1029;
186. Math. USSR-Izv. 23 (1984) 277-305;
187. Global asymptotic operators of a regular representation, Dokl. Akad. Nauk SSSR 257 (1981) 33-37;
188. Soviet Math. Dokl. 23 (1981) 228-232.
189. M. V. Karasev and V. P. Maslov, Nonlinear Poisson Brackets. Geometry and Quantization (Nauka, Moscow, 1991).
190. M. V. Karasev, Quantization and intrinsic dynamics, in Asymptotic Methods for Wave and Quantum Problems, Amer. Math. Soc. Transl. Ser. 2, Vol. 208 (Amer. Math. Soc., Providence, 2003), pp. 1-32, preprint math-ph/0207047;
191. M. V. Karasev, T. A. Osborn, Quantum, Magnetic algebra and magnetic curvature, preprint quant-ph/0311053.
192. A. A. Kirillov, Elements of the theory of representations. 2nd edn. (Nauka, Moscow, 1978) in Russian;
193. English translation of the 1st edition: Grundlehren Math. Wissensch., Band 220 (Springer, Berlin-New York, 1976).
194. A. A. Kirillov, Geometric quantization, in Dynamical Systems IV, Encyclopaedia Math. Sci., Vol. 4 (Springer, Berlin, 2001), pp. 139-176.
195. J. R. Klauder, Continuous representations and path integrals, revisited, in Path Integrals and Their Applications in Quantum, Statistical and Solid State Physics, Proc. NATO Advanced Study Inst., State Univ. Antwerp, Antwerp, 1977, NATO Adv. Study Inst. Ser., Ser. B: Physics, Vol. 43 (Plenum, New York-London, 1978), pp. 5-38.
196. S. Klimek and A. Lesniewski, Quantum Riemann surfaces, I: The unit disc, Commun. Math. Phys. 146 (1992) 103-122.
197. S. Klimek and A. Lesniewski, Quantum Riemann surfaces, II: The discrete series, Lett. Math. Phys. 24 (1992) 125-139;
198. Quantum Riemann surfaces, III: The exceptional cases, Lett. Math. Phys. 32 (1994) 45-61.
199. E. A. Kochetov and V. S. Yarunin, Coherent-state path integral for transition amplitude: A theory and applications, Phys. Scripta 51 (1995) 46-53.
200. J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965) 269-305.
201. M. Kontsevich, Deformation quantization of Poisson manifolds, preprint q-alg/9709040 (1997).
202. B. Kostant, Quantization and Unitary Representations, Lecture Notes in Math., Vol. 170 (Springer, Berlin, 1970).
203. B. Kostant, Symplectic Spinors, Symposia Mathematica Vol. 14 (Academic Press, London, 1974), pp. 139-152.
204. B. Kostant, On the definition of quantization, in Géométrie Symplectique et Physique Mathématique, Aix-en-Provence, 1974, Colloq. Internat. CNRS, Vol. 237 (Éditions Centre Nat. Recherche Sci., Paris, 1975), pp. 187-210.
205. B. Kostant and S. Sternberg, Symplectic reduction, BRS cohomology, and infinite-dimensional Clifford algebras, Ann. Phys. 176 (1987) 49-113.
206. C. N. Ktorides and L. C. Papaloucas, A special construction of Berezin's L-kernel, Found. Phys. 17 (1987) 201-207.
207. N. P. Landsman, Strict quantization of coadjoint orbits, J. Math. Phys. 39 (1998) 6372-6383.
208. N. P. Landsman, Classical and quantum representation theory, in Proc. Seminar 1980-1990 Mathem. Struct. in Field Theory, Amsterdam, CWI Syllabi, Vol. 39, Math. Centrum (Centrum Wisk. Inform. Amsterdam, 1996), pp. 135-163.
209. N. P. Landsman, Mathematical Topics between Classical and Quantum Mechanics (Springer, New York, 1998).
210. N. P. Landsman, Lie grupoid C* -algebras arid Weyl quantization. Commun. Math. Phys. 206 (1999) 367-381.
211. N. P. Landsman, Quantization and the tangent grupoid, in Operator Algebras and Mathematical Physics, Constanţa, 2001 (Theta, Bucharest, 2003), pp. 251-265, preprint math-ph/0208004.
212. J. M. Leinaas and J. Myrheirn, On the theory of identical particles, Nuovo Cimento B37 (1977) 1-23.
213. W. Lisiecki, Kähler coherent states orbits for representations of semisimple Lie groups, Ann. Inst. H. Poincaré 53 (1990) 857-890.
214. M. A. Lledo, Deformation quantization of coadjoint orbits, Int. J. Mod. Phys. B14 (2000) 2397 2400, preprint math.QA/0003142.
215. G. W. Mackey, Induced Representations of Groups and Quantum Mechanics (Benjamin, New York, 1968).
216. M. S. Marinov, Path integrals on homogeneous manifolds, J. Multi. Phys. 36 (1995) 2458-2469;
217. D. Bar-Moshe and M. S. Marinov, Berezin quantization and unitary representations of Lie groups, Transl. Amer. Math. Soc. 177 (1996) 1-21.
218. V. P. Maslov and O. Yu. Shvedov, Geometric quantization in the Fock space, in Topics in Statistical and Theoretical Physics, AMS Transl. Ser. 2, Vol. 177 (AMS, Providence, 1996), pp. 123-157.
219. R. Menikoff and D. H. Sharp, A gauge invariant formulation of quantum electrodynamics using local currents, J. Math. Phys. 18 (1977) 471-482.
220. A. S. Mishchenko, B. Yu. Sternin and V. E. Shatalov, Lagrangian Manifolds and the Method of the Canonical Operator (Nauka, Moscow, 1978).
221. P. K. Mitter, Stochastic approach to Euclidean quantum field theory, in New Perspectives in Quantum Field Theories, Jaca, 1985 (World Scientific, Singapore, 1986), pp. 189-207.
222. I. Mladenov, Quantization on curved manifolds, in Geometry, Integrability and Quantization, Varna, 2001 (Coral Press, Sofia, 2002), pp. 64-104.
223. C. Moreno, *-products on some Kähler manifolds, Lett. Math. Phys. 11 (1986) 361-372;
224. Invariant star products and representations of compact semisimple Lie groups, Lett. Math. Phys. 12 (1986) 217-229;
225. Geodesic symmetries and invariant star products on Kähler symmetric spaces, Lett. Math. Phys. 13 (1987) 245-257.
226. C. Moreno and P. Ortega-Navarro, Deformations of the algebra of functions on Hermitian symmetric spaces resulting from quantization, Ann. Inst. H. Poincaré Sect. A (N.S.) 38 (1983) 215-241.
227. U. A. Mueller, Zur Quantisierung physikalischer Systeme mit inneren Freiheitsgraden, doctoral dissertation, Technische Universität Clausthal, Clausthal, 1987.
228. I. Mykytiuk, Geometric quantization: Hilbert space structure on the space of generalized sections, Rep. Math. Phys. 43 (1999) 257-266.
229. M. Namiki, Basic Ideas of Stochastic Quantization, Progr. Theoret. Phys. Suppl. 111 (1993) 1-41;
230. Stochastic quantization, Lecture Notes in Physics. New Series m:
231. K. Namsrai, Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics (D. Reidel, Dordrecht-Boston, 1986).
232. P. Nattermann, Dynamics in Borel quantization: Nonlinear Sdirödinger equations vs. Master Equations, doctoral dissertation, Technische Universität Clausthal, Clausthal 1997.
233. E. Nelson, Operants: A functional calculus for non-commuting operators, in Functional Analysis and Related Fields, ed. F. E. Browder (Springer-Verlag, New York, 1970), pp. 172-187.
234. E. Nelson, Quantum Fluctuations (Princeton University Press, Princeton, 1985). What is stochastic mechanics? Mathématiques finitaires et analyse non standard, Publ. Math. University Paris VII, Vol. 31 (Univ. Paris VII, Paris, 1989), pp. 1-4.
235. R. Nest and B. Tsygan, Algebraic index theory, Commun. Math. Phys. 172 (1995) 223-262;
236. Algebraic index theory for families, Adv. Math. 113 (1995) 151-205.
237. D. L. Neuhoff, The other asymptotic theory of lossy source, coding, in Coding and Quantization, Piscataway, NJ, 1992 DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Vol. 14 (AMS, Providence, 1993), pp. 55-65.
238. N. Neumaier, Local ν-Euler derivations and Dclignes characteristic class of Pedosov star products and star products of special type. Commun. Math. Phys. 230 (2002) 271-288, preprint math.QA/9905176;
239. Universality of Fedosov's construction for star products of Wick type on psuudo-Kähler manifolds. Rep. Math. Phys. 52 (2003) 43-80, preprint math.QA/0204031.
240. J. von Neumann, Mathematical foundations of Quantum Mechanics (Princeton University Press, Princeton, 1955).
241. M. Nishioka, Geometric quantization of curved phase space, Hadronic J. 5 (1981/82) 207-213.
242. A. Odzijewicz, On reproducing kernels and quantization of states, Commun. Math. Phys. 114 (1988) 577-597.
243. A. Odzijewicz, Coherent states and geometric quantization, Commun. Math. Phys. 150 (1992) 385-413.
244. A. Odzijewicz, Covariant and contravariant Berezin symbols of bounded operators, Quantization and infinite-dimensional systems, Bialowieza, 1993, eds. J.-P. Antoine, S. T. Ali, W. Lisiecki, I. M. Mladenov and A. Odzijewicz (Plenum, New York, 1994), pp. 99-108.
245. A. Odzijewicz, Coherent state method in geometric quantization, in Twenty Years of Bialowieza: A Mathematical Anthology (Aspects of Differential Geometric Methods in Physics), eds. S. T. Ali, G. G. Emch, A. Odzijewicz, M. Schlichenmaier and L. Woronowicz (World Scientific, Singapore, 2005), pp. 47-78.
246. A. Odzijewicz and M. Świȩtochowski, Coherent states map for mic-kepler system, J. Math. Phys. 38 (1997) 5010-5030.
247. H. Omori, Y. Maeda and A. Yoshioka, Weyl manifolds and deformation quantization, Adv. Math. 85 (1991) 224-255.
248. E. Onofri, A note on coherent state representation of Lie groups, J. Math. Phys. 16 (1975) 1087-1089.
249. B. Ørsted and G. Zhang, Weyl quantization and tensor products of Fock and Bergman spaces, Indiana Univ. Math. J. 43 (1994) 551-582.
250. G. Parisi and Y. S. Wu, Perturbation theory without gauge fixing, Sci. Sinica 24 (1981) 483-496;
251. reprinted in Current topics in Chinese science, Section A - Physics, Vol. 1, pp. 09-82.
252. F. B. Pasemann, Eine geometrische Methode der Quantisierung: Vektorfelddarstellungen, doctoral dissertation, Technische Universität Clausthal, Clausthal, 1977.
253. Z. Pasternak-Winiarski, On reproducing kernels for holomorphic: vector bundles, in Quantization and Infinite-Dimensional Systems, Bialowieza, 1993, eds. J.-P. Antoine, S. T. Ali, W. Lisiecki, I. M. Mladenov and A. Odzijewicz (Plenum, New York, 1994), pp. 109-112.
254. Z. Pasternak-Winiarski and J. Wojcieszynski, Bergman spaces and kernels for holomorphic vector bundles, Demonstr. Math. 30 (1997) 199-214.
255. Z. Pasternak-Winiarski, On the dependence of the reproducing kernel on the weight of integration, J. Funct. Anal. 94 (1990) 110 134;
256. On the dependence of the Bergman section on deformations of the volume form and the Hermitian structure, in Singularity Theory Seminar (Institute of Mathematics, Warsaw University of Technology, 1996), preprint.
257. G. Patissier, Quantification d'un variété symplectique, in Séminaire de Géométrie, 1985-1986; Publ. Dép. Math. Nouvelle Sér. B, 86-4 (University Claude-Bernard, Lyon, 1986), pp. 35-54.
258. J. Peetre, The Berezin transform and Ha-plitz operators, J. Operator Theory 24 (1990) 165-186.
259. J. Peetre and G. Zhang, A weighted Plancherel formula III. The case of hyperbolic matrix ball, Collect. Math. 43 (1992) 273-301.
260. A. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986).
261. J. C. T. Pool, Mathematical aspects of the Weyl correspondence, J. Math. Phys. 7 (1966) 66-76.
262. E. Prugovečki, Consistent formulation of relativistic dynamics for massive spin-zero particles in external fields, Phys. Rev. D18 (1978) 3655-3673.
263. E. Prugovečki, Stochastic Quantum Mechanics and Quantum Spacetime (D. Reidel, Dordrecht-Boston, 1984).
264. M. Puta, Hamiltonian Mechanical Systems and Geometric Quantization, Mathematics arid Its Applications, Vol. 260 (Kluwer, Dordrecht, 1993).
265. F. Radulescu, The Γ-equivariant form of the Berezin quantization of the upper half-plane, Mem. Amer. Math. Soc. 133(630) (1998);
266. Quantum dynamics and Berezin's deformation quantization, in Operator Algebras and Quantum Field Theory, Rome, 1996 (Intern. Press, Cambridge, MA, 1998), pp. 383-389.
267. J. H. Rawnsley, On the cohomology groups of a polarization and diagonal quantization, Trans. Amer. Math. Soc. 230 (1977) 235-255.
268. J. H. Rawnsley, Coherent states and Kähler manifolds, Quarterly J. Math. Oxford 28 (1977) 403-415.
269. J. H. Rawnsley, On the pairing of polarizations, Commun. Math. Phys. 58 (1978) 1-8.
270. J. H. Rawnsley, A nonunitary pairing of polarizations for the Kepler problem, Trans. Amer. Math. Soc. 250 (1979) 167-180.
271. c structures and geometric quantization, Mem. Amer. Math. Soc. 81(410) (1989).
272. N. Reshetikhin and L. Takhtajan, Deformation quantization of Kähler manifolds, in L.D. Faddeev's Seminar on Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, Vol. 201 (Amer. Math. Soc., Providence, 2000), pp. 257-276, preprint math/9907171.
273. M. A. Rieffel, Deformation quantization and operator algebras, in Operator Theory: Operator Algebras and Applications, Durham, NH, 1988, Proc. Symp. Pure Math. Vol. 51 (1900), pp. 411-423.
274. M. A. Rieffel, Quantization and C*-algebras, C*-algebras: 1943-1993 (San Antonio, 1993) Contemp. Math. Vol. 167 (AMS, Providence, 1994), pp. 66-97.
275. d, Mem. Amer. Math. Soc. 106(506) (1993).
276. M. A. Rieffel, Questions on quantization, in Operator Algebras and Operator Theory, Shanghai, 1997, Contemp. Math., Vol. 228 (AMS, Providence, 1998), pp. 315-326.
277. P. L. Robinson, A cohomological pairing of half-forms, Trans. Amer. Math. Soc. 301 (1987) 251-261.
278. P. L. Robinson, A report on geometric quantization, in Differential Geometry: Partial Differential Equations on Manifolds, Los Angeles. 1990, Proc. Symp. Pure. Math. Vol. 54, Part 1 (Amer. Math. Soc., Providence, 1993), pp. 403-415.
279. D. J. Rowe, Quantization using vector coherent state methods, Quantisation. Coherent States, and Poisson Structures, Bialowieza, 1995 (PWN, Warsaw, 1998). pp. 157-175;
280. S. D. Bartlett, D. J. Rowe and J. Repka, Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations, J. Phys. A: Math. Gen. 35 (2002) 5599-5623, preprint quant-ph/0201129;
281. Vector coherent state representations, induced representations, and geometric quantization: II. Vector coherent state representations, J. Phys. A: Math. Gen. 35 (2002) 5625-5651, preprint quant-ph/0201130;
282. D. J. Rowe and J. Repka, Coherent state triplets and their inner products, J. Math. Phys. 43 (2002) 5400-5438, preprint math-ph/0205034.
283. M. Schlichenmaier, Deformation quantization of compact Kähler manifolds by Berezin-Toeplitz quantization, in Conference Moshé Flato 1999, Dijon, France 1999, Vol. 2 (Kluwer. 2000), pp. 289-306, preprint math.QA/9910137;
284. Zwei Anwendungen algebraisch-geometrischer Methoden in der theoretischen Physik: Berezin-Toeplitz Quantisierung und globale Algebren der zweidimensionalen konformen Feldtheorie, Habilitation thesis, Mannheim, 1996.
285. M. Schlichenmaier, Deformation quantization of compact Kähler manifolds via Berezin-Toeplitz operators, in Group Theoretical Methods in Physics, Goslar, 1996 (World Scientific, 1997), pp. 396-400;
286. Berezin-Toeplitz quantization of compact Kähler manifolds, Quantization, Coherent States and Poisson Structures, Bialowieza, 1995, PWN (1998), pp. 101-115, preprint q-alg/9601016;
287. Berezin-Toeplitz quantization and Berezin symbols for arbitrary compact Kähler manifolds, in Coherent States, Quantization and Gravity, Bialowieza, 1998, eds. M. Schlichenmaier, A. Strasburger, S. T. Ali and A. Odzijewicz (Warsaw University Press, 2001), 45-56, preprint math.QA/9902066.
288. I. E. Segal, Quantization of nonlinear systems, J. Math. Phys. 1 (1960) 468-488.
289. I. A. Šereševskii, Quantization in cotangent bundles, Dokl. Akad. Nauk SSSR 245 (1979) 1057-1060 (in Russian);
290. Soviet Math. Dokl. 20 (1979) 402-405.
291. M. A. Shubin, Pseudodifferential Operators and Spectral Theory (Nauka, Moscow, 1978); English translation (Springer-Verlag, Berlin, 1987).
292. R. Simon, E. C. G. Sudarshan and N. Mukunda, Gaussian pure states in quantum mechanics and the symplectic group, Phys. Rev. A37 (1988) 3028-3038.
293. D. J. Simms, An outline of geometric quantization (d'après Kostant), in Differential Geometrical Methods in Mathematical Physics, Bonn, 1975, Lecture Notes in Math., Vol. 570 (Springer, Berlin, 1977), pp. 1-10.
294. D. J. Simms and N. M. J. Woodhouse, Lectures on Geometric Quantization, Lecture Notes in Physics, Vol. 53 (Springer, New York, 1976).
295. R. Sjamaar, Symplectic reduction and Riemann-Roch formulas for multiplicities, Bull. Amer. Math. Soc. 33 (1996) 327-338.
296. J. Sniatycki, On geometric quantization of classical systems, in Mathematical Foundations of Quantum Theory, Loyola Univ., New Orleans, 1977 (Acad. Press New York 1978), pp. 287-297.
297. J. Sniatycki, Geometric Quantization and Quantum Mechanics (Springer-Verlag, Berlin, 1980).
298. J. Sniatycki, Constraints and Quantization, Lecture Notes in Math., Vol. 1087 (1983), pp. 293-310.
299. J.-M. Souriau, Structure, des Systémes Dynamiques, Dunod, Paris 1969
300. English translation Structure of Dynamical Systems, Progr. Math., Vol. 149 (Birkhäuser, Boston, 1997).
301. J.-M. Souriau, Groupes différentiels, Differential geometrical methods in mathematical physics (Aix-en-Provence/Salamanca, 1979). pp. 91-128. Lecture Notes in Math., Vol. 836 (Springer, Berlin-New York, 1980).
302. J.-M. Souriau, Quantification géométrique, Physique Quantique et Géométrie (Paris, 1986), Travaux en Cours, Vol. 32 (Hermann, Paris, 1988), pp. 141-193.
303. J.-M. Souriau, Des particules aux ondes: Quantification géométrique, in Huyghen's Principle 1690-1990: Theory and Applications, The Hague and Scheveningen, 1990, Stud. Math. Phys., Vol. 3 (North-Holland, Amsterdam, 1992), pp. 299-341.
304. D. Sternheimer, Deformation quantization: Twenty years after, in Particles, Fields and Gravitation, Lodz, 1998, AIP Conf. Proc., Vol. 453 (Amer. Inst. Phys., Woodbury, 1998), pp. 107-145;
305. Star products: Their ubiquity and unicity, in Modern. Group Theoretical Methods in Physics, Paris, 1995, Math. Phys. Stud., Vol. 18 (Kluwer, Dordrecht, 1995), pp. 255-265.
306. M. Takesaki, Tomita's Theory of Modular Hilbert Algebras and its Application, Lecture Notes in Math., Vol. 128 (Springer, Berlin, 1970).
307. M. E. Taylor, Pseudodifferential Operators (Princeton University Press, Princeton, 1981).
308. Y. Tian and W. Zhang, An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg, Invent. Math. 132 (1998) 229-259.
309. J. Tolar, Borel Quantization and the origin of topological effects in quantum mechanics, in Differential Geometry, Group Representations, and Quantization, Lecture Notes in Phys., Vol. 379 (Springer, Berlin, 1991), pp. 179-190.
310. G. M. Tuynman, Geometric quantization, in Proceedings Seminar 1983-1985: Mathematical Structures in Field Theories, Vol. 1, CWI Syllabus, Vol. 8 (Math. Centrum, CWI, Amsterdam, 1985).
311. G. M. Tuynman, Generalized Bergman kernels and geometric quantization, J. Math. Phys. 28 (1987) 573-583.
312. G. M. Tuynman, Quantization: Towards a comparison between methods, J. Math. Phys. 28 (1987) 2829-2840.
313. G. M. Tuynman, What are the rules of the game called BRST?, in Proc. Mathematical Aspects of Classical Field Theory, Seattle, WA, 1991, Contemp. Math., Vol. 132 (AMS, Providence, 1992), pp. 625-633.
314. G. M. Tuynman, What is prequantization, and what is geometric quantization?, in Mathematical Structures in Field Theory, Proc. Seminar 1989-1990, CWI Syllabi, Vol. 39 (Math. Centrum, CWI, Amsterdam), pp. 1-28 (1996).
315. G. M. Tuynman, Prequantization is irreducible, Pub. IRMA, Lille, 37 (1995), no. XV, 1-13;
316. Indag. Math. (N.S.) 9 (1998) 607-618.
317. A. Unterberger, Encore des classes de symboles, Séminaire Goulaouic-Schwartz (1977/1978), Exp. No. 6 (École Polytech., Palaiseau, 1978).
318. A. Unterberger, Quantification des certains espaces Hermitiens symétriques, Séminaire Goulaouic-Schwartz 1979/1980, Exp. No. 16 (École Polytech., Palaiseau, 1980).
319. A. Unterberger, The calculus of pseudodifferential operators of Fuchs type, Comm. Partial Dig. Equations 9 (1984) 1179-1236.
320. A. Unterberger. Pseudodifferential analysis, quantum mechanics and relativity. Comm. Partial Diff. Equations 13 (1988) 847 894;
321. Quantification relativiste, Mem. Soc. Math. France (N.S.) 44-45 (1991);
322. Quantization, symmetries and relativity, in Perspectives on Quantization, South Hadley, 1990; Contemp. Math. Vol. 214 (AMS, Providence, 1998), pp. 169-187.
323. A. Unterberger, Quantization: Some problems, tools, and applications, in Operator Theory and Complex and Hypercomplex Analyati, Mexico City, 1994, Contemp. Math., Vol. 212 (AMS, Providence, 1998). pp. 285-298.
324. A. Unterberger, Composition formulas associated with symbolic calculi and applications, preprint ESI No. 822 (http://www.esi.ac.at/ESI-Preprints.html), Erwin-Schrödinger-Institute, Wien (1999).
325. A. Unterberger arid H. Upmeier, Pseudodifferential Analysis on Symmetric Cones (CRC Press, Boca Raton, 1996).
326. H. Upmeier, Weyl quantization on symmetric spaces I. Hyperbolic matrix domains, J. Funct. Anal. 96 (1991) 297-330;
327. Weyl quantization of complex domains, in Operator Algebras and Topology, Craiova, 1989, Pitman Research Notes in Math., Vol. 270 (Longman Harlow, 1992), pp. 160-178.
328. V. S. Varadarajan, Geometry of Quantum Theory (Springer-Vorlag, New York, 1985).
329. M. Vergue, Geometric: quantization and equivariant cohomology, in First European Congress of Mathematicians, Paris, 1992, Vol. 1. Progress in Math. 119 (Birkhauser, Boston, 1994), pp. 249-295.
330. M. Vergne, Convex polytopes and quantization of symplectic manifolds, Proc. Natl. Acad. Sci. USA 93 (1996) 14238-14242.
331. M. Vergne, Quantification géométrique et réduction symplectique, Séminaire Bourbaki 2000/2001, Astérisque 282 (2002), Exp. no. 888, 249-278.
332. D. A. Vogan, Jr., Noncommutative algebras and unitary representations, The mathematical heritage of Hermann Weyl (Durham, NC, 1987), pp. 35-60, Proc. Symp. Pure Math., Vol. 48, AMS, Providence, 1988.
333. A. Weil, Variétés Kählériennes (Hermann, Paris, 1958).
334. P. B. Wiegmann, Multivalued functionals and geometrical approach for quantization of relativistic particles and strings, Nuclear Phys. B323 (1989) 311-329.
335. A. Weinstein, Symplectic groupoids, geometric quantization, and irrational rotation algebras, Symplectic geometry, groupoids, and integrable systems (Berkeley, 1989), pp. 281-290, Math. Sci. Res. Inst. Publ., Vol. 20 (Springer, New York, 1991).
336. A. Weinstein, Deformation quantization, Séminaire Bourbaki, exposé 789, Astérisque 227 (1994) 389-409.
337. H. Weyl, The Theory of Groups and Quantum Mechanics, (Dover, New York, 1931).
338. N. Woodhouse, Geometric Quantization (Clarendon Press, Oxford, 1980).
339. N. M. J. Woodhouse, Geometric Quantization, 2nd edn. Oxford Math. Monographs (Clarendon Press, Oxford University Press, New York, 1992).
340. S. Zakrzewski, Geometric quantization of Poisson groups - diagonal and soft deformations, in Symplectic Geometry and Quantization, Sanda and Yokohama, 1993, Contemp. Math., Vol. 179 (AMS, Providence, 1994), pp. 271-285.
341. S. Zelditch, Szegö kernels and a theorem of Tian, Int. Math. Res. Not. 6 (1998) 317-331.
342. Q. Zhao, Quantum kinematics and geometric quantization, J. Geom. Phys. 21 (1996) 34-42.