zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Geometric quantization of presymplectic manifolds. (English) Zbl 0521.58035

53D50Geometric quantization
37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
53C80Applications of global differential geometry to physics
[1]Abraham, R., Marsden, J. E.: Foundations of Mechanics, 2nd Ed. Reading, Mass.: Benjamin/Cummings Publ. Comp. 1978.
[2]Aldaya, V., de Azc?rraga, J. A.: Quantization as a consequence of the symmetry group: An approach to geometric quantization. J. Math. Phys.23, 1297-1305 (1982). · Zbl 0502.58018 · doi:10.1063/1.525513
[3]de Barros, C. M.: Sur la g?ometrie diff?rentielle des formes diff?rentielles ext?rieures quadratiques. In: Atti Convegno Intern. Geometria Differenziale, Bologna 1967, pp. 117-142. Bologna: Ed. Zanichelli. 1967.
[4]Gotay, M. J.: On coisotropic imbeddings of presymplectic manifolds. Preprint. Univ. Calgary. 1980.
[5]Gotay, M. J., ?niatycki, J.: On the quantization of presymplectic dynamical systems via coisotropic imbeddings. Comm. Math. Phys.82, 377-389 (1981). · Zbl 0508.58024 · doi:10.1007/BF01237045
[6]G?nther, C.: Presymplectic manifolds and the quantization of relativistic particle systems. In: Differential Geometrical Methods in Mathematical Physics, Proc. Conf. Salamanca 1979, pp. 383-400. Lecture Notes Math. 836. Berlin-Heidelberg-New York: Springer. 1980.
[7]Lichnerowicz, A.: Les vari?t?s de Poisson et leurs alg?bres de Lie associ?es. J. Diff. Geom.12, 253-300 (1977).
[8]Sasaki, S.: On the differential geometry of tangent bundles of Riemannian manifolds. T?hoku Math. J.10, 338-345 (1958). · Zbl 0086.15003 · doi:10.2748/tmj/1178244668
[9]Satake, I.: The Gauss-Bonnet theorem forV-manifolds. J. Math. Soc. Japan9, 464-492 (1957). · Zbl 0080.37403 · doi:10.2969/jmsj/00940464
[10]?niatycki, J.: Geometric Quantization and Quantum Mechanics. Berlin-Heidelberg-New York: Springer. 1980.
[11]?niatycki, J.: Constraints and Quantization. Preprint. Univ. Calgary. 1982.
[12]Souriau, J. M.: Structures des Syst?mes Dynamiques. Paris: Dunod. 1970.
[13]Vaisman, I.: Cohomology and Differential Forms. New York-Basel: M. Dekker. 1973.
[14]Vaisman, I.: Basic ideas of geometric quantization. Rend. Sem. Mat. Torino37, 31-41 (1979).
[15]Vaisman, I.: A coordinatewise formulation of geometric quantization. Ann. Inst. H. Poincar?31, 5-24 (1979).
[16]Woodhouse, N.: Geometric Quantization. Oxford: Clarendon, Press. 1980.
[17]Yano, K.: The Theory of Lie Derivatives and its Applications. Amsterdam: North Holland. 1957.