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.
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.
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://archive.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://archive.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://archive.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, Volume 60 (2010) no. 1, pp. 51-85. doi : 10.5802/aif.2517. http://archive.numdam.org/articles/10.5802/aif.2517/
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