Introduction to Representations of the Canonical Commutation and Anticommutation Relations
Page 1 Introduction to Representations of the Canonical Commutation and Anticommutation …

Abstract The Dirac–Fock (DF) model replaces the Hartree–Fock (HF) approximation in
quantum chemistry when relativistic effects cannot be neglected. Since the Dirac operator is …

We give a review of semi-classical estimates for bound states and their eigenvalues for
Schrödinger operators. Motivated by the classical results, we discuss their recent …

We study the energy of relativistic electrons and positrons interacting via the second
quantized Coulomb potential in the field of a nucleus of charge Z within the Hartree-Fock …

Jansen and Heß--correcting an earlier paper of Douglas and Kroll--have derived a (pseudo-
) relativistic energy expression which is very successful in describing heavy atoms. It is an …

For ν∈[0, 1]⁠, let D ν be the distinguished self-adjoint realisation of the three-dimensional
Coulomb-Dirac operator− i α⋅∇− ν|⋅|− 1⁠. For ν∈[0, 1)⁠, we prove the lower bound of the …

We show that the Douglas-Kroll block-diagonalization method for the Dirac operator with
Coulomb potential is convergent in norm resolvent sense for coupling constant γ less than γ …

Perturbative Implementation of the Furry Picture Page 1 DOI 10.1007/s11005-006-0127-x Letters
in Mathematical Physics (2007) 79:99–108 © Springer 2006 Perturbative Implementation of the …

A mathematically consistent formulation of relativistic quantum electrodynamics (QED) has
still to be found. Nevertheless, there are several simplified effective models that successfully …

Cette thèse est consacrée à l'étude de trois modèles non linéaires issus de la mécanique
quantique. Dans la première partie, nous démontrons l'existence d'un minimum et d'états …