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The spinless semi-relativistic Pauli-Fierz Hamiltonian $H$ in quantum electrodynamics is considered. The self-adjointness and essential self-adjointness of $H$ are shown. It is emphasized that it includes the massless case. Furthermore, the…

We consider the semi-relativistic Pauli-Fierz Hamiltonian and a no-pair model of a hydrogen-like atom interacting with a quantized photon field at the respective critical values of the Coulomb coupling constant. For arbitrary values of the…

HVZ type theorem for semi-relativistic Pauli-Fierz Hamiltonian, $$\HHH=\sqrt{(p\otimes \one -A)^2+M^2}+V\otimes \one +\one\otimes \hf,\quad M\geq 0,$$ in quantum electrodynamics is studied. Here $H$ is a self-adjoint operator in Hilbert…

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…

Generalized Pauli-Fierz Hamiltonian with Kato-class potential $\KPF$ in nonrelativistic quantum electrodynamics is defined and studied by a path measure. $\KPF$ is defined as the self-adjoint generator of a strongly continuous one-parameter…

We prove a general theorem about the self-adjointness and domain of Pauli-Fierz type Hamiltonians. Our proof is based on commutator arguments which allow us to treat fields with non-commuting components. As a corollary it follows that the…

We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues…

We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues…

We consider the semi-relativistic Pauli-Fierz Hamiltonian $$ H_m = |{\bf p}-{\bf A}({\bf x})| + H_{f,m} + V({\bf x}),\quad m\geq0, $$ and prove the existence of the ground state of $H_m$ for $m=0$. Here ${\bf A}({\bf x})$ denotes a…

We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of the semi-relativistic Pauli-Fierz operator and prove that the infimum of the spectrum of the latter operator is an eigenvalue. In particular,…

A semi-relativistic Pauli-Fierz model is defined by the sum of the free Hamiltonian $H_{\rm f}$ of a Boson Fock space, an nuclear potential $V$ and a relativistic kinetic energy: $$ H=\sqrt{[\sigma\cdot(\mathbf{p}+e\mathbf{A})]^2+M^2} - M +…

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…

In this work we present a set of virial relations for many electron systems coupled to field modes, described by the Pauli--Fierz Hamiltonian in dipole approximation and using length gauge. Currently, there is growing interest in solutions…

In this article, we review the general quantum mechanical setting associated to a non self-adjoint Hamiltonian with real spectrum. Spectral properties of the Hamiltonian of a simple model of the Swanson type are investigated. The…

A Feynman-Kac-type formula for a L\'evy and an infinite dimensional Gaussian random process associated with a quantized radiation field is derived. In particular, a functional integral representation of $e^{-t\PF}$ generated by the…

A translation invariant Hamiltonian $H$ in the nonrelativistic quantum electrodynamics is studied. This Hamiltonian is decomposed with respect to the total momentum $\tot$: $$H=\int_{\BR} ^\oplus \fri(P) dP,$$ where the self-adjoint fiber…

In this paper, we consider the spectrum of a model in quantum electrodynamics with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint; (2) under the infrared regularity condition, the Hamiltonian has a unique ground…

We consider a charged particle, spin 1/2, with relativistic kinetic energy and minimally coupled to the quantized Maxwell field. Since the total momentum is conserved, the Hamiltonian admits a fiber decomposition as $H(P)$, $P\in \BbbR^3$.…

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…

Several proposals to deal with the dynamics of general relativity involve gauge fixings or the introduction matter fields in terms of which the theory is deparameterized. The resulting theories have true Hamiltonians for their evolution…