Connes' tangent groupoid and strict quantization

We address one of the open problems in quantization theory recently listed by Rieffel. By developing in detail Connes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict flabby quantization, which is moreover an asymptotic morphism and satisfies th...

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Detalles Bibliográficos
Autores: Cariñena Marzo, José F., Clemente Gallardo, Jesús, Follana, Eduardo, Gracia Bondía, José M., Rivero, Alejandro, Várilly Boyle, Joseph C.
Tipo de recurso: artículo
Fecha de publicación:1999
País:Costa Rica
Institución:Universidad de Costa Rica
Repositorio:Kérwá
Idioma:inglés
OAI Identifier:oai:kerwa.ucr.ac.cr:10669/87831
Acceso en línea:https://www-sciencedirect-com/science/article/pii/S039304409800028X
https://hdl.handle.net/10669/87831
Access Level:acceso abierto
Palabra clave:geometría no conmutativa
grupoide tangente
cuantización de Moyal
MATEMÁTICAS
Descripción
Sumario:We address one of the open problems in quantization theory recently listed by Rieffel. By developing in detail Connes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict flabby quantization, which is moreover an asymptotic morphism and satisfies the reality and traciality constraints, on any oriented Riemannian manifold. That construction generalizes the standard Moyal rule. The paper can be considered as an introduction to quantization theory from Connes' point of view.