We consider a spinless particle coupled to a photon field and prove that even if the Schrödinger operator $p^2 + V$ does not have eigenvalues the system can have a ground state. We describe the coupling by means of the Pauli-Fierz Hamiltonian and our result holds in the case where the coupling constant $α$ is small.
We consider scattering of a single photon by an atom or a molecule in the framework of non relativistic qed, and we express the scattering matrix for one photon scattering as a boundary value of the resolvent.
We consider the ground state and the ground state energy of an atom with spinless electrons in the framework of non-relativistic qed. We show that the ground state energy as well as the ground state depend analytically on the parameters of the group of dilations, the parameter of a group of spatial dependent phase changes, and on the minimal coupling constant. As a corollary we obtain spatial exponential decay of the ground state as well as of its dilation analytic extension. No infrared regularization is needed for the result. Our result is based on operator theoretic renormalization.
An enhanced binding of $N$-{\it relativistic} particles coupled to a massless scalar bose field is investigated. It is not assumed that the system has a ground state for the zero-coupling. It is shown, however, that there exists a ground state for sufficiently large coupling. The proof is based on checking the stability condition and showing a uniform exponential decay of infrared regularized ground states.
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 $u\otimes Ψ_f$, where $u$ is a normalized state for the electron and $Ψ_f$ is a coherent state in Fock space for the photon field. The minimization of this functional yields a Maxwell--Schr{ö}dinger system up to a trivial renormalization. We prove the existence of a ground state under general conditions on the external potential and the coupling. In particular, neit…
Employing recent results on stochastic differential equations associated with the standard model of non-relativistic quantum electrodynamics by B. Güneysu, J.S. Møller, and the present author, we study the continuity of the corresponding semi-group between weighted vector-valued L^p-spaces, continuity properties of elements in the range of the semi-group, and the pointwise continuity of an operator-valued semi-group kernel. We further discuss the continuous dependence of the semi-group and its integral kernel on model parameters. All these results are obtained for Kato decomposable electrostat…
We consider a Haag-Kastler net in a positive energy representation, admitting massive Wigner particles and asymptotic fields of massless bosons. We show that states of the massive particles are always vacua of the massless asymptotic fields. Our argument is based on the Mean Ergodic Theorem in a certain extended Hilbert space. As an application of this result we construct the outgoing isometric wave operator for Compton scattering in QED in a class of representations recently proposed by Buchholz and Roberts. In the course of this analysis we use our new technique to further simplify scatterin…
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 previous work that an electron alone can bind due to the vacuum polarization, under some technical assumptions. Here we prove the absence of binding for the system of two electrons: the response of the vacuum is not sufficient to counterbalance the repulsion of the electrons.
