Introduction aux méthodes euclidiennes en théorie quantique des champs
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...
Itô calculus and quantisation of Lie bialgebras
Itô versus Woronowicz calculus in Itô Hopf algebras
Le spin et la relativité restreinte
Maps into and applications
Markov product of positive definite kernels and applications to Q-matrices of graph products
We show positivity of the Q-matrix of four kinds of graph products: direct product (Cartesian product), star product, comb product, and free product. During the discussion we give an alternative simple proof of the Markov product theorem on positive definite kernels.
Markovian bridges and reversible diffusion processes with jumps
Martin boundary theory of some quantum random walks
Measure solutions for semilinear evolution equations with polynomial growth and their optimal control
In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.
Measures connected with Bargmann's representation of the q-commutation relation for q > 1
Classical Bargmann’s representation is given by operators acting on the space of holomorphic functions with scalar product . We consider the problem of representing the functional F as a measure. We prove the existence of such a measure for q > 1 and investigate some of its properties like uniqueness and radiality.
Méthodes de noyaux et de symboles en calcul stochastique non commutatif
Mild solutions of quantum stochastic differential equations.
Non-Hermitian quantum mechanics with minimal length uncertainty.
Number operator algebras.
On essential self-adjointness of the relativistic hamiltonian of a spinless particle in a negative scalar potential
On Hopf algebra deformation approach to renormalization.