Related papers: Mass Renormalization and Energy Level Shift in Non…
We study three well known models of matter coupled to the ultraviolet cutoff, quantized radiation field and to the Coulomb potential of arbitrarily many nuclei. Two are nonrelativistic: the first uses the kinetic energy (p+eA(x))^2 and the…
We investigate the ground state energy of an electron coupled to a photon field. First, we regard the self-energy of a free electron, which we describe by the Pauli-Fierz Hamiltonian. We show that, in the case of small values of the…
This work addresses the problem of infrared mass renormalization for a scalar electron in a translation-invariant model of non-relativistic QED. We assume that the interaction of the electron with the quantized electromagnetic field…
We prove enhanced binding and increase of binding energies in the non- and semi-relativistic Pauli-Fierz models, for arbitrary values of the fine-structure constant and the ultra-violet cut-off, and discuss the resulting improvement of…
We investigate the self-energy of one electron coupled to a quantized radiation field by extending the ideas developed recently by C. Hainzl. We fix an arbitrary cut-off parameter Lambda and recover the alpha^2-term of the self-energy,…
The purpose of these notes is to provide a pedagogical introduction to the concept of renormalization in atomic physics. We study quantum dynamics of a model of a nonrelativistic single electron atom coupled to the quantum radiation field…
In this paper, we determine the exact expression for the hydrogen binding energy in the Pauli-Fierz model up to the order $O(\alpha^5\log\alpha^{-1})$, where $\alpha$ denotes the finestructure constant, and prove rigorous bounds on the…
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…
We consider a non-relativistic electron bound by an external potential and coupled to the quantized electromagnetic field in the standard model of non-relativistic QED. We compute the energy functional of product states of the form…
We consider a translation-invariant Pauli-Fierz model describing a non-relativistic charged quantum mechanical particle interacting with the quantized electromagnetic field. The charged particle may be spinless or have spin one half. We…
The massless fermion limit of QED is discussed. For on-shell renormalisation the high energy behaviour fixes no lower limit on the mass of the lightest fermion if the fine structure constant $\alpha$ is allowed to vary. The choice of an…
Within the framework of nonrelativisitic quantum electrodynamics we consider a single nucleus and $N$ electrons coupled to the radiation field. Since the total momentum $P$ is conserved, the Hamiltonian $H$ admits a fiber decomposition with…
We study the ground state energy of the Pauli--Fierz model in the absence of external potentials. We consider the fiber decomposition of the Pauli--Fierz operator with respect to the spectral values, $p$, of the total momentum operator and…
In nonrelativistic QED the charge of an electron equals its bare value, whereas the self-energy and the mass have to be renormalized. In our contribution we study perturbative mass renormalization, including second order in the fine…
The effective mass $\mass$ of the the Pauli-Fierz Hamiltonain with ultraviolet cutoff $\Lambda$ and the bare mass $m$ in nonrelativistic QED with spin 1/2 is investigated. Analytic properties of $\mass$ in coupling constant $e$ are shown…
The electron-electron interaction correction of first order in $1/Z$ to the one-electron part of the nuclear recoil effect on binding energies in atoms and ions is considered within the framework of the rigorous QED approach. The…
The quantum electrodynamics formalism to treat the interelectronic-interaction correction of first order in $1/Z$ to the two-electron part of the nuclear recoil effect on binding energies in atoms and ions is developed. The nonperturbative…
We consider the semi-relativistic Pauli-Fierz model for a single free electron interacting with the quantized radiation field. Employing a variant of Pizzo's iterative analytic perturbation theory we construct a sequence of ground state…
We look at an electron in the field of an arbitrary external potential $V$, such that the Schr\"odinger operator $p^2 + V$ has at least one eigenvalue, and show that by coupling to a quantized radiation field the binding energy increases,…
The Pauli-Fierz model $H(\alpha)$ in nonrelativistic quantum electrodynamics is considered. The external potential $V$ is sufficiently shallow and the dipole approximation is assumed. It is proven that there exist constants $0<\alpha_-<…