RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1984, Volume 39, Issue 6(240), Pages 115–173 (Mi umn2505)  

This article is cited in 46 scientific papers (total in 46 papers)

Asymptotic and geometric quantization

M. V. Karasev, V. P. Maslov


Full text: PDF file (3929 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1984, 39:6, 133–205

Bibliographic databases:

UDC: 517.9
MSC: 81S10, 53D50, 53D55, 47G30, 81R15
Received: 23.06.1982

Citation: M. V. Karasev, V. P. Maslov, “Asymptotic and geometric quantization”, Uspekhi Mat. Nauk, 39:6(240) (1984), 115–173; Russian Math. Surveys, 39:6 (1984), 133–205

Citation in format AMSBIB
\Bibitem{KarMas84}
\by M.~V.~Karasev, V.~P.~Maslov
\paper Asymptotic and geometric quantization
\jour Uspekhi Mat. Nauk
\yr 1984
\vol 39
\issue 6(240)
\pages 115--173
\mathnet{http://mi.mathnet.ru/umn2505}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=771100}
\zmath{https://zbmath.org/?q=an:0588.58031}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1984RuMaS..39..133K}
\transl
\jour Russian Math. Surveys
\yr 1984
\vol 39
\issue 6
\pages 133--205
\crossref{https://doi.org/10.1070/RM1984v039n06ABEH003183}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984ATQ3200004}


Linking options:
  • http://mi.mathnet.ru/eng/umn2505
  • http://mi.mathnet.ru/eng/umn/v39/i6/p115

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Karasev, “Analogues of the objects of Lie group theory for nonlinear Poisson brackets”, Math. USSR-Izv., 28:3 (1987), 497–527  mathnet  crossref  mathscinet  zmath
    2. M. V. Karasev, “Poisson symmetry algebras and the asymptotics of spectral series”, Funct. Anal. Appl., 20:1 (1986), 17–26  mathnet  crossref  mathscinet  zmath  isi
    3. A. G. Savinkov, “Topological charges in field theories with broken symmetry”, Theoret. and Math. Phys., 71:2 (1987), 463–473  mathnet  crossref  mathscinet  isi
    4. A. Yu. Khrennikov, “Functional superanalysis”, Russian Math. Surveys, 43:2 (1988), 103–137  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. A. Yu. Khrennikov, “The correspondence principle in quantum field theory and relativistic boson string theory”, Math. USSR-Sb., 67:1 (1990), 209–233  mathnet  crossref  mathscinet  isi
    6. A. Yu. Khrennikov, “The Central Limit Theorem for a Quasi-Gaussian Distribution on an Infinite-Dimensional Superspace”, Theory Probab Appl, 35:3 (1990), 580  mathnet  crossref  mathscinet  zmath  isi
    7. B. V. Fedosov, “Deformation quantization and asymptotic operator representation”, Funct. Anal. Appl., 25:3 (1991), 184–194  mathnet  crossref  mathscinet  zmath  isi
    8. E. I. Zelenov, “$p$-Adic quantum mechanics and coherent states”, Theoret. and Math. Phys., 86:2 (1991), 143–151  mathnet  crossref  mathscinet  zmath  isi
    9. Hideki Omori, Yoshiaki Maeda, Akira Yoshioka, “Weyl manifolds and deformation quantization”, Advances in Mathematics, 85:2 (1991), 224  crossref
    10. Agostino Prástaro, “Quantum geometry of PDE's”, Reports on Mathematical Physics, 30:3 (1991), 273  crossref
    11. V. V. Belov, S. Yu. Dobrokhotov, “Semiclassical maslov asymptotics with complex phases. I. General approach”, Theoret. and Math. Phys., 92:2 (1992), 843–868  mathnet  crossref  mathscinet  isi
    12. A. Yu. Daletskii, “Infinite-dimensional Schrödinger equations and the representation of a group of symplectomorphisms of a Hilbert phase space”, Funct. Anal. Appl., 26:1 (1992), 74–75  mathnet  crossref  mathscinet  zmath  isi
    13. V V Belov, V M Olive, J L Volkova, J Phys A Math Gen, 28:20 (1995), 5799  crossref  mathscinet  zmath  adsnasa  isi
    14. M. V. Karasev, E. M. Novikova, “Representation of exact and semiclassical eigenfunctions via coherent states. Hydrogen atom in a magnetic field”, Theoret. and Math. Phys., 108:3 (1996), 1119–1159  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. Sergio Albeverio, Alexei Daletskii, “Asymptotic quantization for solution manifolds of some infinite dimensional Hamiltonian systems”, Journal of Geometry and Physics, 19:1 (1996), 31  crossref
    16. Sergio Albeverio, Alexei Daletskh, “Algebras of Pseudodifferential Operators inL2 Given by Smooth Measures on Hilbert Spaces”, Math Nachr, 192:1 (1998), 5  crossref  mathscinet  zmath  isi
    17. M Karasev, “Advances in quantization: quantum tensors, explicit star-products, and restriction to irreducible leaves”, Differential Geometry and its Applications, 9:1-2 (1998), 89  crossref  elib
    18. Mikhail Karasev, Yuri Vorobjev, “Integral Representations over Isotropic Submanifolds and Equations of Zero Curvature”, Advances in Mathematics, 135:2 (1998), 220  crossref
    19. Fani Petalidou, “Sur la symplectisation de structures bihamiltoniennes”, Bulletin des Sciences Mathématiques, 124:4 (2000), 255  crossref
    20. V. V. Belov, O. S. Dobrokhotov, S. Yu. Dobrokhotov, “Isotropic Tori, Complex Germ and Maslov Index, Normal Forms and Quasimodes of Multidimensional Spectral Problems”, Math. Notes, 69:4 (2001), 437–466  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    21. 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
    22. Bruning, J, “The spectral asymptotics of the two-dimensional Schrodinger operator with a strong magnetic field. II”, Russian Journal of Mathematical Physics, 9:4 (2002), 400  mathscinet  isi
    23. Bruning, J, “The spectral asymptotics of the two-dimensional Schrodinger operator with a strong magnetic field. I”, Russian Journal of Mathematical Physics, 9:1 (2002), 14  mathscinet  isi
    24. V. V. Belov, S. Yu. Dobrokhotov, V. A. Maksimov, “Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application”, Theoret. and Math. Phys., 135:3 (2003), 765–791  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    25. V. V. Belov, S. Yu. Dobrokhotov, T. Ya. Tudorovskii, “Asymptotic Solutions of Nonrelativistic Equations of Quantum Mechanics in Curved Nanotubes: I. Reduction to Spatially One-Dimensional Equations”, Theoret. and Math. Phys., 141:2 (2004), 1562–1592  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    26. M. V. Karasev, E. M. Novikova, “Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field”, Theoret. and Math. Phys., 141:3 (2004), 1698–1724  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    27. M V Karasev, T A Osborn, “Cotangent bundle quantization: entangling of metric and magnetic field”, J Phys A Math Gen, 38:40 (2005), 8549  crossref  mathscinet  zmath  adsnasa  isi  elib
    28. O. N. Grigor'ev, M. V. Karasev, “Dynamical equations for the quantum product on a symplectic space in affine coordinates”, Math. Notes, 77:1 (2005), 39–47  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    29. S. Albeverio, S. Mazzucchi, “Generalized Fresnel integrals”, Bulletin des Sciences Mathématiques, 129:1 (2005), 1  crossref
    30. J. Brüning, S. Dobrokhotov, S. Sekerzh-Zenkovich, T. Tudorovskiy, “Spectral series of the Schrödinger operator in thin waveguides with periodic structure, I adiabatic approximation and semiclassical asymptotics in the 2D case”, Russ J Math Phys, 13:4 (2006), 380  crossref  mathscinet  isi  elib
    31. A Vourdas, “Analytic representations in quantum mechanics”, J Phys A Math Gen, 39:7 (2006), R65  crossref  mathscinet  zmath  adsnasa  isi
    32. M.V. Karasev, T.A. Osborn, “Magnetic quantization over Riemannian manifolds”, Can. J. Phys, 84:6-7 (2006), 551  crossref  elib
    33. M. I. Krivoruchenko, Amand Faessler, “Weyl’s symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics”, J Math Phys (N Y ), 48:5 (2007), 052107  crossref  mathscinet  zmath  adsnasa  isi
    34. M. V. Karasev, “Internal geometric current, and the Maxwell equation as a Hamiltonian system on configuration surfaces”, Russ J Math Phys, 14:2 (2007), 134  crossref  mathscinet  zmath  isi  elib
    35. J. Brüning, S. Yu. Dobrokhotov, R. V. Nekrasov, T. Ya. Tudorovskiy, “Quantum dynamics in a thin film, I. Propagation of localized perturbations”, Russ. J. Math. Phys, 15:1 (2008), 1  crossref
    36. S. P. Baranovskii, I. V. Shirokov, “Deformations of vector fields and canonical coordinates on coadjoint orbits”, Siberian Math. J., 50:4 (2009), 580–586  mathnet  crossref  mathscinet  isi  elib
    37. A. Yu. Anikin, “Quantum Birkhoff normal forms”, Theoret. and Math. Phys., 160:3 (2009), 1274–1291  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    38. Karasev, MV, “Quantum geometry and quantum mechanics of integrable systems”, Russian Journal of Mathematical Physics, 16:1 (2009), 81  crossref  mathscinet  zmath  adsnasa  isi  elib
    39. Mattias Marklund, Jens Zamanian, Gert Brodin, “Spin Kinetic Theory—Quantum Kinetic Theory in Extended Phase Space”, Transport Theory and Statistical Physics, 39:5-7 (2011), 502  crossref
    40. A. V. Pereskokov, “Asymptotics of the Spectrum and Quantum Averages near the Boundaries of Spectral Clusters for Perturbed Two-Dimensional Oscillators”, Math. Notes, 92:4 (2012), 532–543  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    41. A. V. Pereskokov, “Asymptotics of the spectrum of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters”, Trans. Moscow Math. Soc., 73 (2012), 221–262  mathnet  crossref  mathscinet  zmath  elib
    42. A. V. Pereskokov, “Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters”, Izv. Math., 77:1 (2013), 163–210  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    43. A. V. Pereskokov, “Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters”, Theoret. and Math. Phys., 178:1 (2014), 76–92  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    44. M. V. Karasev, E. M. Novikova, “Eigenstates of the quantum Penning–Ioffe nanotrap at resonance”, Theoret. and Math. Phys., 179:3 (2014), 729–746  mathnet  crossref  crossref  adsnasa  isi  elib
    45. A. V. Pereskokov, “Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator”, Math. Notes, 101:6 (2017), 1009–1022  mathnet  crossref  crossref  mathscinet  isi  elib
    46. D. B. Zotev, “Predkvantovanie po Kostantu simplekticheskikh mnogoobrazii s kontaktnymi osobennostyami”, Matem. zametki, 105:6 (2019), 857–878  mathnet  crossref
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:883
    Full text:353
    References:62
    First page:7

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019