Geometric quantization of integrable systems with hyperbolic singularities

Mark D. Hamilton[1]; Eva Miranda[2]

  • [1] Graduate School of Mathematical Sciences University of Tokyo 3-8-1 Komaba Meguro-Ku Tokyo 153-8914 (Japan)
  • [2] Universitat Autònoma de Barcelona 08193 Bellaterra (Spain)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 1, page 51-85
  • ISSN: 0373-0956

Abstract

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We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we compute the effect of hyperbolic singularities, which make an infinite-dimensional contribution to the quantization, thus showing that this quantization depends strongly on polarization.

How to cite

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Hamilton, Mark D., and Miranda, Eva. "Geometric quantization of integrable systems with hyperbolic singularities." Annales de l’institut Fourier 60.1 (2010): 51-85. <http://eudml.org/doc/116273>.

@article{Hamilton2010,
abstract = {We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we compute the effect of hyperbolic singularities, which make an infinite-dimensional contribution to the quantization, thus showing that this quantization depends strongly on polarization.},
affiliation = {Graduate School of Mathematical Sciences University of Tokyo 3-8-1 Komaba Meguro-Ku Tokyo 153-8914 (Japan); Universitat Autònoma de Barcelona 08193 Bellaterra (Spain)},
author = {Hamilton, Mark D., Miranda, Eva},
journal = {Annales de l’institut Fourier},
keywords = {Geometric quantization; integrable system; non-degenerate singularity; geometric quantization; moment map; prequantum line bundle; non-singular Bohr-Sommerfeld leaf},
language = {eng},
number = {1},
pages = {51-85},
publisher = {Association des Annales de l’institut Fourier},
title = {Geometric quantization of integrable systems with hyperbolic singularities},
url = {http://eudml.org/doc/116273},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Hamilton, Mark D.
AU - Miranda, Eva
TI - Geometric quantization of integrable systems with hyperbolic singularities
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 1
SP - 51
EP - 85
AB - We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we compute the effect of hyperbolic singularities, which make an infinite-dimensional contribution to the quantization, thus showing that this quantization depends strongly on polarization.
LA - eng
KW - Geometric quantization; integrable system; non-degenerate singularity; geometric quantization; moment map; prequantum line bundle; non-singular Bohr-Sommerfeld leaf
UR - http://eudml.org/doc/116273
ER -

References

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