[Quantification géométrique des systèmes intégrables avec singularités hyperboliques]
On construit la quantification géométrique d’une surface compacte en utilisant une polarisation singulière donnée par un système intégrable. Cette polarisation présente toujours des singularités qu’on suppose de type non-dégénéré. En particulier, on calcule l’effet des singularités hyperboliques qui donnent une contribution de dimension infinie à la quantification, en démontrant que cette quantification dépend fortement de la polarisation choisie.
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.
Keywords: Geometric quantization, integrable system, non-degenerate singularity
Mot clés : quantification géométrique, système intégrable, singularité non-dégénérée
@article{AIF_2010__60_1_51_0,
author = {Hamilton, Mark D. and Miranda, Eva},
title = {Geometric quantization of integrable systems with hyperbolic singularities},
journal = {Annales de l'Institut Fourier},
pages = {51--85},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {60},
number = {1},
year = {2010},
doi = {10.5802/aif.2517},
zbl = {1191.53058},
mrnumber = {2664310},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2517/}
}
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 SP - 51 EP - 85 VL - 60 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2517/ DO - 10.5802/aif.2517 LA - en ID - AIF_2010__60_1_51_0 ER -
%0 Journal Article %A Hamilton, Mark D. %A Miranda, Eva %T Geometric quantization of integrable systems with hyperbolic singularities %J Annales de l'Institut Fourier %D 2010 %P 51-85 %V 60 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2517/ %R 10.5802/aif.2517 %G en %F AIF_2010__60_1_51_0
Hamilton, Mark D.; Miranda, Eva. Geometric quantization of integrable systems with hyperbolic singularities. Annales de l'Institut Fourier, Tome 60 (2010) no. 1, pp. 51-85. doi : 10.5802/aif.2517. http://www.numdam.org/articles/10.5802/aif.2517/
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