相关论文: The Mean-Field Approximation in Quantum Electrodyn…
The Bogoliubov-Dirac-Fock (BDF) model is the mean-field approximation of no-photon Quantum Electrodynamics. The present paper is devoted to the study of the minimization of the BDF energy functional under a charge constraint. An associated…
The Bogoliubov-Dirac-Fock (BDF) model allows to describe relativistic electrons interacting with the Dirac sea. It can be seen as a mean-field approximation of Quantum Electro-dynamics (QED) where photons are neglected. This paper treats…
We study the Bogoliubov-Dirac-Fock (BDF) model, a no-photon, mean-field approxi- mation of quantum electrodynamics that allows to study relativistic electrons interacting with the vacuum. It is a variational model in which states are…
We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum…
In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles…
To obtain the basis for combining various many-body techniques to QED in a consistent manner, we investigate the theory of quantum electrodynamical self-consistent fields. The reserch interest was born mainly of the electronic structure…
We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles like electrons and of the Dirac sea which is self-consistently polarized in the presence of the real particles. The…
Nonlinear electrodynamics, QED included, is considered against the Lorentz-noninvariant external field background, treated as an anisotropic medium. Hamiltonian formalism is applied to electromagnetic excitations over the background, and…
This paper studies the model of the quantum electrodynamics (QED) of a single nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P. Blanchard. This model exhibits infrared divergence in a very simple context. The…
The Bogoliubov-Dirac-Fock (BDF) model is a no-photon, mean-field approxi- mation of quantum electrodynamics. It describes relativistic electrons in the Dirac sea. In this model, a state is fully characterized by its one-body density matrix,…
Certain gauge transformations may act non-trivially on physical states in quantum electrodynamics (QED). This observation has sparked the yet unresolved question of how to characterize allowed boundary conditions for gauge theories. Faddeev…
Hartree-Fock approximation suffers from two inabilities including i) the divergence of electron Fermi velocity , and ii) existence of bandwidth not confirmed experimentally. Here, we study the effects of minimal length on the ground state…
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 approximation. We show that the associated functional has a…
In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of…
At energies much less than the electron mass $m$ the effects of quantum fluctuations in the vacuum due to virtual electron loops can be included by extending the Maxwell Lagrangian by additional non-renormalizable terms corresponding to the…
We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field limiting regime, the dynamics is described by the Hartree-Fock equation. This extends previous work of Bardos et al. to the case of…
We derive the ground state energy up to the fourth order in the fine structure constant $\alpha$ for the translation invariant Pauli-Fierz Hamiltonian for a spinless electron coupled to the quantized radiation field. As a consequence, we…
We study the Bogoliubov-Dirac-Fock model which is a mean-field approximation of QED. It allows to consider relativistic electrons interacting with the Dirac sea. We study the system of two electrons in the vacuum: it has been shown in a…
Studying the electronic structure of defects in materials is an important subject in condensed matter physics. From a mathematical point of view, nonlinear mean-field models of localized defects in insulators are well understood. We present…
The problem of gauge invariance in an ultraviolet complete quantum field theory (QFT) with nonlocal interactions is investigated. For local fields that couple through a nonlocal interaction, it is demonstrated that the quantum…