Geometric Quantization and Multiplicities of Group Representations.
Geometry of the Kepler system in coherent states approach
Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group
Let be a quasi-Hermitian Lie group with Lie algebra and be a compactly embedded subgroup of . Let be a regular element of which is fixed by . We give an explicit -equivariant diffeomorphism from a complex domain onto the coadjoint orbit of . This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where is associated with a unitary irreducible representation of which is holomorphically...
Hamiltonian reduction and quantization on symplectic manifolds.
Hypercontractivité pour les fermions, d'après Carlen-Lieb
Index and dynamics of quantized contact transformations
Quantized contact transformations are Toeplitz operators over a contact manifold of the form , where is a Szegö projector, where is a contact transformation and where is a pseudodifferential operator over . They provide a flexible alternative to the Kähler quantization of symplectic maps, and encompass many of the examples in the physics literature, e.g. quantized cat maps and kicked rotors. The index problem is to determine when the principal symbol is unitary, or equivalently to determine...
Introduction to noncommutative differential geometry.
Invariant symbolic calculus for compact Lie groups
We study the invariant symbolic calculi associated with the unitary irreducible representations of a compact Lie group.
Invariant symbolic calculus for semidirect products
Let be the semidirect product where is a connected semisimple non-compact Lie group acting linearly on a finite-dimensional real vector space . Let be a unitary irreducible representation of which is associated by the Kirillov-Kostant method of orbits with a coadjoint orbit of whose little group is a maximal compact subgroup of . We construct an invariant symbolic calculus for , under some technical hypothesis. We give some examples including the Poincaré group.
Isospectrality for quantum toric integrable systems
We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...
On Hopf algebra deformation approach to renormalization.
On quantum vector fields in general relativistic quantum mechanics.
Particles in the superworldline and BRST
In this short note we discuss -supersymmetric worldlines of relativistic massless particles and review the known result that physical spin- fields are in the first BRST cohomology group. For , emphasis is given to particular deformations of the BRST differential, that implement either a covariant derivative for a gauge theory or a metric connection in the target space seen by the particle. In the end, we comment about the possibility of incorporating Ramond-Ramond fluxes in the background.
Poisson cohomology and quantization.
Quantification formelle des variétés de Poisson
Quantization and Morita equivalence for constant Dirac structures on tori
We define a -algebraic quantization of constant Dirac structures on tori and prove that -equivalent structures have Morita equivalent quantizations. This completes and extends from the Poisson case a theorem of Rieffel and Schwarz.
Quantization of pencils with a gl-type Poisson center and braided geometry
We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson pencils and...
Quantization of Poisson structures on .
Quantization of the cotangent bundle via the tangent groupoid
Quantization of the orientation preserving automorphisms of the torus