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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr.:

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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 1985, Volume 4, Pages 141–176 (Mi intf35)  

This article is cited in 18 scientific papers (total in 18 papers)

Geometric quantization

A. A. Kirillov

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UDC: 514.8+517.986

Citation: A. A. Kirillov, “Geometric quantization”, Dynamical systems – 4, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 4, VINITI, Moscow, 1985, 141–176

Citation in format AMSBIB
\by A.~A.~Kirillov
\paper Geometric quantization
\inbook Dynamical systems~--~4
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr.
\yr 1985
\vol 4
\pages 141--176
\publ VINITI
\publaddr Moscow

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    This publication is cited in the following articles:
    1. A. A. Kirillov, D. V. Yur'ev, “Kähler geometry of the infinite-dimensional homogeneous manifold $M=\operatorname{Diff}_+(S^1)/\operatorname{Rot}(S^1)$”, Funct. Anal. Appl., 20:4 (1986), 322–324  mathnet  crossref  mathscinet  zmath  isi
    2. D. V. Yur'ev, “Non-Euclidean geometry of mirrors and prequantization on the homogeneous Kähler manifold $M=\operatorname{Diff}_+(S^1)/\operatorname{Rot}(S^1)$”, Russian Math. Surveys, 43:2 (1988), 187–188  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. D. Popov, “Geometric quantization of strings and reparametrization invariance”, Theoret. and Math. Phys., 83:3 (1990), 608–619  mathnet  crossref  mathscinet  isi
    4. A. D. Popov, “Generalized twistors and geometric quantization”, Theoret. and Math. Phys., 87:1 (1991), 331–344  mathnet  crossref  mathscinet  zmath  isi
    5. E. I. Bogdanov, “Quantization of classical lagrangian mechanics”, Theoret. and Math. Phys., 91:3 (1992), 629–633  mathnet  crossref  mathscinet  isi
    6. V. Yu. Ovsienko, C. Roger, “Deformations of Poisson brackets and extensions of Lie algebras of contact vector fields”, Russian Math. Surveys, 47:6 (1992), 135–191  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. S. A. Bychkov, D. V. Yur'ev, “Three algebraic structures of quantum projective ($\mathrm{sl}(2,\mathbb C)$-invariant) field theory”, Theoret. and Math. Phys., 97:3 (1993), 1333–1339  mathnet  crossref  mathscinet  zmath  isi
    8. M. V. Karasev, M. B. Kozlov, “Representations of Compact Semisimple Lie Algebras over Lagrangian Submanifolds”, Funct. Anal. Appl., 28:4 (1994), 238–246  mathnet  crossref  mathscinet  zmath  isi
    9. G. E. Arutyunov, “Representations of the compact quantum group $SU_q(2)$ and geometrical quantization”, Theoret. and Math. Phys., 100:2 (1994), 921–927  mathnet  crossref  mathscinet  zmath  isi
    10. E. I. Bogdanov, “Spatially distributed classical Lagrangian mechanics”, Theoret. and Math. Phys., 101:3 (1994), 1419–1421  mathnet  crossref  mathscinet  zmath  isi
    11. A. N. Tyurin, “On Bohr–Sommerfeld bases”, Izv. Math., 64:5 (2000), 1033–1064  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. A. L. Gorodentsev, A. N. Tyurin, “Abelian Lagrangian algebraic geometry”, Izv. Math., 65:3 (2001), 437–467  mathnet  crossref  crossref  mathscinet  zmath
    13. N. A. Tyurin, “The correspondence principle in Abelian Lagrangian geometry”, Izv. Math., 65:4 (2001), 823–834  mathnet  crossref  crossref  mathscinet  zmath
    14. M. V. Karasev, E. M. Novikova, “Coherent Transforms and Irreducible Representations Corresponding to Complex Structures on a Cylinder and on a Torus”, Math. Notes, 70:6 (2001), 779–797  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. A. G. Sergeev, “Geometricheskoe kvantovanie prostranstv petel”, Sovr. probl. matem., 13, MIAN, M., 2009, 3–294  mathnet  crossref  elib
    16. Thomas Leuther, Fabian Radoux, “Natural and Projectively Invariant Quantizations on Supermanifolds”, SIGMA, 7 (2011), 034, 12 pp.  mathnet  crossref  mathscinet
    17. V. V. Kozlov, “Liouville's equation as a Schrödinger equation”, Izv. Math., 78:4 (2014), 744–757  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. A. G. Sergeev, “O dvukh geometricheskikh zadachakh, voznikayuschikh v matematicheskoi fizike”, Fundament. i prikl. matem., 20:2 (2015), 157–166  mathnet  mathscinet  elib; A. G. Sergeev, “On two geometric problems arising in mathematical physics”, J. Math. Sci., 223:6 (2017), 756–762  crossref
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