Mathematical foundations of geometric quantization.
Multiplicative integrable models from Poisson-Nijenhuis structures
We discuss the role of Poisson-Nijenhuis (PN) geometry in the definition of multiplicative integrable models on symplectic groupoids. These are integrable models that are compatible with the groupoid structure in such a way that the set of contour levels of the hamiltonians in involution inherits a topological groupoid structure. We show that every maximal rank PN structure defines such a model. We consider the examples defined on compact hermitian symmetric spaces studied by F. Bonechi, J. Qiu...
Multiplicity-free complex manifolds.
Natural and projectively invariant quantizations on supermanifolds.
Note sur la méthode des isopérimètres
Notes on prequantization of moduli of -bundles with connection on Riemann surfaces
Let be a smooth proper family of complex curves (i.e. family of Riemann surfaces), and a -bundle over with connection along the fibres . We construct a line bundle with connection on (also in cases when the connection on has regular singularities). We discuss the resulting mainly in the case . For instance when is the moduli space of line bundles with connection over a Riemann surface , , and is the Poincaré bundle over , we show that provides a prequantization of .
O funkcích goniometrických
O ploském obsahu kruhového výkrojku
O vypočítání obsahu komolého jehlance
On quantum de Rham cohomology theory.
On quantum vector fields in general relativistic quantum mechanics.
On some spaces of linear functionals on the algebras for locally compact groups
On the classical and quantum evolution of lagrangian half-forms in phase space
On the geometric prequantization of brackets.
En este artículo se considera un marco general para la precuantización geométrica de una variedad provista de un corchete que no es necesariamente de Jacobi. La existencia de una foliación generalizada permite definir una noción de fibrado de precuantización. Se estudia una aproximación alternativa suponiendo la existencia de un algebroide de Lie sobre la variedad. Se relacionan ambos enfoques y se recuperan los resultados conocidos para variedades de Poisson y Jacobi.
Poisson cohomology and quantization.
Poznámka k vypočítání obsahu trojbokého hranolu šikmého
Poznámka o sférické trigonometrii
Quantification de certains espaces hermitiens symétriques
Quantification d'une variété symplectique
Quantification et approximations semi-classiques