Skip to main content

Reduction and Geometric Prequantization at the Cotangent Level

  • Chapter
Recent Developments in Quantum Mechanics

Part of the book series: Mathematical Physics Studies ((MPST,volume 12))

  • 238 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abraham, R., Marsden, J.: Foundations of mechanics, Second Edition, Addison Wesley 1978.

    MATH  Google Scholar 

  2. Blau, M.: On the geometric quantization of constrained systems, Class.Quantum Gray. 5 (1988) 1033–1044.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Gotay, M.J.: Constraints. Reduction and Quantization, J.Math.Phys. 27, (1986), 2051–2067.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  5. Marsden, J., Weinstein, A.: Reduction of symplectic manifolds with symmetry, Raports on Math.Phys. 5 (1974), 121–130.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Marsden, J., Weinsten, A.: The Hamiltonian structure of the Maxwell-Vlasov equations, Physica 4D (1982), 394–406.

    MATH  Google Scholar 

  7. Puta, M.: On the reduced phase space of a cotangent bundle, Lett.Math.Phys. 8 (1984), 189–194.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Puta, M.: Geometric quantization of the Heavy Top, Lett.Math.Phys. 11 (1986), 105–112, Erratum and Addendum, 12 (1986) 169.

    MathSciNet  Google Scholar 

  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. Puta, M.: On the geometric prequantization of Maxwell-equations, Lett.Math.Phys. 13 (1987) 99–103.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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.

    MathSciNet  Google Scholar 

  12. Puta, M.: Geometric quantization of the sperical pendulum, Serdica Bulgaricae Math.Publ. 14 (1988) 198–201.

    MathSciNet  MATH  Google Scholar 

  13. Puta, M.: Geometric prequantization of the Einstein’s vacuum field equations (to appear).

    Google Scholar 

  14. Puta, M.: Dirac constrained mechanical systems and geometric prequantization (to appear).

    Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  16. Sniatycki, J.: Constraints and quantization, Lect.Notes in Math., vol. 1037 (1983) 301–334.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Puta, M. (1991). Reduction and Geometric Prequantization at the Cotangent Level. In: Boutet de Monvel, A., Dita, P., Nenciu, G., Purice, R. (eds) Recent Developments in Quantum Mechanics. Mathematical Physics Studies, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3282-4_19

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-3282-4_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5449-2

  • Online ISBN: 978-94-011-3282-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics