All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 135

Showing per page

Formal geometric quantization

Paul-Émile Paradan (2009)

Annales de l’institut Fourier

Let K be a compact Lie group acting in a Hamiltonian way on a symplectic manifold ( M , Ω ) which is pre-quantized by a Kostant-Souriau line bundle. We suppose here that the moment map Φ is proper so that the reduced space M μ : = Φ - 1 ( K · μ ) / K is compact for all μ . Then, we can define the “formal geometric quantization” of M as 𝒬 K - ∞ ( M ) : = ∑ μ ∈ K ^ 𝒬 ( M μ ) V μ K . The aim of this article is to study the functorial properties of the assignment ( M , K ) → 𝒬 K - ∞ ( M ) .

Geometric quantization and no-go theorems

Viktor Ginzburg, Richard Montgomery (2000)

Banach Center Publications

A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist. This is a...

Geometric quantization of integrable systems with hyperbolic singularities

Mark D. Hamilton, Eva Miranda (2010)

Annales de l’institut Fourier

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.

Integrable systems and group actions

Eva Miranda (2014)

Open Mathematics

The main purpose of this paper is to present in a unified approach to different results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective.

Invariants symplectiques et semi-classiques des systèmes intégrables avec singularités

San Vũ Ngọc (2000/2001)

Séminaire Équations aux dérivées partielles

On définit les notions de feuilletages classiques et semi-classiques pour les systèmes complètement intégrables avec singularités. Les résultats de classification standard (telles les coordonnées actions-angles semi-classiques) sont rappelés. Le cas du feuilletage classique de type foyer-foyer est examiné en détail, où des nouveaux invariants semi-globaux apparaissent. Ces invariants sont identifiés dans les conditions de Bohr-Sommerfeld singulières qui donnent le spectre conjoint au voisinage d’une...

La trilogie du moment

Patrick Iglesias (1995)

Annales de l'institut Fourier

A toute deux-forme fermée, sur une variété connexe, on associe une famille d’extensions centrales du groupe de ses automorphismes par son tore des périodes. On discute ensuite quelques propriétés de cette construction.

Logarithmic Poisson cohomology: example of calculation and application to prequantization

Joseph Dongho (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure. We prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kähler differentials. Therefore it induces a differential complex from which we derive the notion of logarithmic Poisson cohomology. We prove that Poisson cohomology and logarithmic Poisson cohomology are equal when the Poisson structure is log symplectic. We give an example of...

Maslov indices on the metaplectic group M p ( n )

Maurice De Gosson (1990)

Annales de l'institut Fourier

We use the properties of M p ( n ) to construct functions μ ℓ : M p ( n ) → Z 8 associated with the elements ℓ of the lagrangian grassmannian Λ (n) which generalize the Maslov index on Mp(n) defined by J. Leray in his “Lagrangian Analysis”. We deduce from these constructions the identity between M p ( n ) and a subset of S p ( n ) × Z 8 , equipped with appropriate algebraic and topological structures.

Currently displaying 41 – 60 of 135