Report
Geometric quantization via cotangent models
| Title: | Geometric quantization via cotangent models |
|---|---|
| Authors: | Miranda Galcerán, Eva, Mir Garcia, Pau |
| Contributors: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
| Source: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Publisher Information: | 2022. |
| Publication Year: | 2022 |
| Subject Terms: | contact geometry, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial, Classificació AMS::53 Differential geometry::53D Symplectic geometry, Symplectic geometry, Geometria simplèctica, Symplectic Geometry, Matemàtiques i estadística::Geometria::Geometria diferencial [Àrees temàtiques de la UPC], 53 Differential geometry::53D Symplectic geometry, contact geometry [Classificació AMS], Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry, Mathematical Physics |
| Description: | In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the cotangent models in [KM17] by both considering singular orbits and adding to the cotangent models a model for the prequantum line bundle. These singularities are generic in the sense that are given by Morse-type functions and include elliptic, hyperbolic and focus-focus singularities. Examples of systems admitting such singularities are toric, semitoric and almost toric manifolds, as well as physical systems such as the coupling of harmonic oscillators, the spherical pendulum or the reduction of the Euler’s equations of the rigid body on T *(SO(3)) to a sphere. Our geometric quantization formulation coincides with the models given in [HM10] and [MPS20] away from the singularities and corrects former models for hyperbolic and focus-focus singularities cancelling out the infinite dimensional contributions obtained by former approaches. The geometric quantization models provided here match the classical physical methods for mechanical systems such as the spherical pendulum as presented in [CS16]. Our cotangent models obey a local-to-global principle and can be glued to determine the geometric quantization of the global systems even if the global symplectic classification of the systems is not known in general. |
| Document Type: | Report |
| File Description: | application/pdf |
| Language: | English |
| Access URL: | http://hdl.handle.net/2117/365667 https://hdl.handle.net/2117/365667 https://hdl.handle.net/2117/365667 https://arxiv.org/abs/2102.02699 |
| Accession Number: | edsair.dedup.wf.002..2e851ddc62faee0d45607566a0ce49e2 |
| Database: | OpenAIRE |
| Description not available. |