Geometric Quantization on Manifolds

  • Brian C. Hall
Part of the Graduate Texts in Mathematics book series (GTM, volume 267)


Geometric quantization is a type of quantization, which is a general term for a procedure that associates a quantum system with a given classical system. In practical terms, if one is trying to deduce what sort of quantum system should model a given physical phenomenon, one often begins by observing the classical limit of the system. Electromagnetic radiation, for example, is describable on a macroscopic scale by Maxwell’s equations. On a finer scale, quantum effects (photons) become important. How should one determine the correct quantum theory of electromagnetism? It seems that the only reasonable way to proceed is to “quantize” Maxwell’s equations—and then to compare the resulting quantum system to experiment.


Line Bundle Symplectic Manifold Cotangent Bundle Geometric Quantization Vertical Polarization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [4].
    R.J. Blattner, Quantization and representation theory. In Harmonic Analysis on Homogeneous Spaces (Proceedings of Symposia in Pure Mathematics, vol. XXVI, Williams College, Williamstown, MA, 1972). (American Mathematical Society, Providence, RI, 1973), pp. 147–165Google Scholar
  2. [20].
    B.C. Hall, Geometric quantization and the generalized Segal–Bargmann transform for Lie groups of compact type. Comm. Math. Phys. 226, 233–268 (2002)CrossRefMATHMathSciNetGoogle Scholar
  3. [29].
    J. Lee, Introduction to Smooth Manifolds, 2nd edn. (Springer, London, 2006)Google Scholar
  4. [45].
    N. Woodhouse, Geometric Quantization, 2nd edn. (Oxford University Press, Oxford, 1992)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Brian C. Hall
    • 1
  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA

Personalised recommendations