Degenerate space-time paths and the non-locality of quantum mechanics in a Clifford substructure of space-time.
Deligne-Beilinson cohomology and abelian link invariants.
Dense point spectrum and absolutely continuous spectrum in spherically symmetric Dirac operators.
Derivation of Hartree’s theory for mean-field Bose gases
This article is a review of recent results with Phan Thành Nam, Nicolas Rougerie, Sylvia Serfaty and Jan Philip Solovej. We consider a system of bosons with an interaction of intensity (mean-field regime). In the limit , we prove that the first order in the expansion of the eigenvalues of the many-particle Hamiltonian is given by the nonlinear Hartree theory, whereas the next order is predicted by the Bogoliubov Hamiltonian. We also discuss the occurrence of Bose-Einstein condensation in these...
Dérivations, formes et opérateurs usuels sur les champs spinoriels des variétés différentiables de dimension paire
Derivations of quasi -algebras.
Derivations of the Moyal algebra and noncommutative gauge theories.
Des ponts
Description lagrangienne d'un boson scalaire à l'aide d'un triplet nucléaire
Determinantal representation of the time-dependent stationary correlation function for the totally asymmetric simple exclusion model.
Développement asymptotique de la densité d'états pour des opérateurs de Schrödinger aléatoires singuliers
Développements asymptotiques dans l'approximation de Born-Oppenheimer
Développements asymptotiques des perturbations lentes de l'opérateur de Schrödinger périodique
Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique
Diamagnetic behavior of sums Dirichlet eigenvalues
The Li-Yau semiclassical lower bound for the sum of the first eigenvalues of the Dirichlet–Laplacian is extended to Dirichlet– Laplacians with constant magnetic fields. Our method involves a new diamagnetic inequality for constant magnetic fields.
Differential calculus on almost commutative algebras and applications to the quantum hyperplane
In this paper we introduce a new class of differential graded algebras named DG -algebras and present Lie operations on this kind of algebras. We give two examples: the algebra of forms and the algebra of noncommutative differential forms of a -algebra. Then we introduce linear connections on a -bimodule over a -algebra and extend these connections to the space of forms from to . We apply these notions to the quantum hyperplane.
Differential calculus on 'non-standard' (h-deformed) Minkowski spaces
The differential calculus on 'non-standard' h-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are simultaneously hermitian.
Differential geometry over the structure sheaf: a way to quantum physics
An idea for quantization by means of geometric observables is explained, which is a kind of the sheaf theoretical methods. First the formulation of differential geometry by using the structure sheaf is explained. The point of view to get interesting noncommutative observable algebras of geometric fields is introduced. The idea is to deform the algebra by suitable interaction structures. As an example of such structures the Poisson-structure is mentioned and this leads naturally to deformation...
Differential pseudoconnections and field theories
Differential representations of dynamical oscillator symmetries in discrete Hilbert space.