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Reduction and Geometric Prequantization at the Cotangent Level

  • Mircea Puta
Chapter
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Part of the Mathematical Physics Studies book series (MPST, volume 12)

Abstract

Let (M,ω) be a symplectic manifold (possibly infinite dimensional), G a Lie group (possibly infinite dimensional) with Lie algebra G and Ø :G M → M a symplectic action of G on M, with and Ad * -equivariant momentum map J: M → G *i.e.

Keywords

Symplectic Manifold Cotangent Bundle Geometric Quantization Reduce Phase Space Hamiltonian Vector Field 
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References

  1. [1]
    Abraham, R., Marsden, J.: Foundations of mechanics, Second Edition, Addison Wesley 1978.zbMATHGoogle Scholar
  2. [2]
    Blau, M.: On the geometric quantization of constrained systems, Class.Quantum Gray. 5 (1988) 1033–1044.MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. [3]
    Gotay, M.J.: Constraints. Reduction and Quantization, J.Math.Phys. 27, (1986), 2051–2067.MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. [4]
    Kummer, M.: On the construction of the reduced phase space of a Hamiltonian system with symmetry, Indiana Univ.Math.Journ. 30 (1981), 281–291.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Marsden, J., Weinstein, A.: Reduction of symplectic manifolds with symmetry, Raports on Math.Phys. 5 (1974), 121–130.MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. [6]
    Marsden, J., Weinsten, A.: The Hamiltonian structure of the Maxwell-Vlasov equations, Physica 4D (1982), 394–406.zbMATHGoogle Scholar
  7. [7]
    Puta, M.: On the reduced phase space of a cotangent bundle, Lett.Math.Phys. 8 (1984), 189–194.MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. [8]
    Puta, M.: Geometric quantization of the Heavy Top, Lett.Math.Phys. 11 (1986), 105–112, Erratum and Addendum, 12 (1986) 169.MathSciNetGoogle Scholar
  9. [9]
    Puta, M.: Geometric quantization of the reduced phase space of the cotangent bundle, Proceedings of the Conference 24–30 August (1986) Brno, Czechoslovakia, Brno (1987), 273–282.Google Scholar
  10. [10]
    Puta, M.: On the geometric prequantization of Maxwell-equations, Lett.Math.Phys. 13 (1987) 99–103.MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. [11]
    Puta, M.: The planar n-body problem and geometric quantization, The XVIII-th National Conference on Geometry and Topology, Oradea-Felix, October 4–7, 1987, Preprint No. 2 (1988), 151–154.MathSciNetGoogle Scholar
  12. [12]
    Puta, M.: Geometric quantization of the sperical pendulum, Serdica Bulgaricae Math.Publ. 14 (1988) 198–201.MathSciNetzbMATHGoogle Scholar
  13. [13]
    Puta, M.: Geometric prequantization of the Einstein’s vacuum field equations (to appear).Google Scholar
  14. [14]
    Puta, M.: Dirac constrained mechanical systems and geometric prequantization (to appear).Google Scholar
  15. [15]
    Satzer, M.J.: Canonical reduction of mechanical systems invariant under abelian group actions with an application to celestical mechanics, Indiana Univ.Math.Journ. 26 (1977), 951–976.MathSciNetzbMATHCrossRefGoogle Scholar
  16. [16]
    Sniatycki, J.: Constraints and quantization, Lect.Notes in Math., vol. 1037 (1983) 301–334.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • Mircea Puta
    • 1
  1. 1.Department of Geometry-TopologyUniversity of TimişoaraTimişoaraRomania

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