#### Filter Results:

- Full text PDF available (31)

#### Publication Year

1993

2014

- This year (0)
- Last 5 years (6)
- Last 10 years (14)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

We consider a system of finitely many nonrelativistic, quantum mechanical electrons bound to static nuclei. The electrons are minimally coupled to the quantized electromagnetic field; but we impose an ultraviolet cutoff on the electromagnetic vector potential appearing in covariant derivatives, and the interactions between the radiation field and electrons… (More)

- Volker Bach
- 2000

We consider systems of static nuclei and electrons {atoms and molecules{ coupled to the quantized radiation eld. The interactions between electrons and the soft modes of the quantized electromagnetic eld are described by minimal coupling, ~ p! ~ p e ~ A(~x), where ~ A(~x) is the electromagnetic vector potential with an ultraviolet cuto . If the interactions… (More)

- Volker Bach, Thomas Chen, Jürg Fröhlichy, Israel Michael Sigalz
- 2003

A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map. It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel… (More)

- Volker Bach
- 1997

In this paper we present a self-contained and detailed exposition of the new renormalization group technique proposed in [1, 2]. Its main feature is that the renormalization group transformation acts directly on a space of operators rather than on objects such as a propagator, the partition function, or correlation functions. We apply this renormalization… (More)

- Volker Bach, Elliott H. Lieb, Michael Loss, Jan Philip Solovej
- 1994

We prove that in an exact, unrestricted Hartree-Fock calculation each energy level of the Hartree-Fock equation is either completely lled or completely empty. The only assumption needed is that the two-body interaction is| like the Coulomb interaction|repulsive; it could, however, be more complicated than a simple potential, e.g., it could have tensor… (More)

In this paper we study the energy spectrum of the Pauli-Fierz Hamiltonian generating the dynamics of nonrelativistic electrons bound to static nuclei and interacting with the quantized radiation eld. We show that, for su ciently small values of the elementary electric charge, and under weaker conditions than those required in [3], the spectrum of this… (More)

- Volker Bach, Fb Mathematik, Y S Ma, J Frr, Israel Michael Sigal
- 1995

We consider a system of nitely many non-relativistic electrons bound in an atom or molecule which are coupled to the electromagnetic eld via minimal coupling or the dipole approximation. Among a variety of results, we give suucient conditions for the existence of a ground state (an eigenvalue at the bottom of the spectrum) and resonances (eigenvalues of a… (More)

- Jens Schulze, Volker Bach, Hubert Österle
- HMD - Praxis Wirtschaftsinform.
- 2000

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 comprises a fixed ultraviolet regularization and an infrared regularization parametrized by σ > 0. For the value p = 0 of the… (More)

- Volker Bach
- 1996

We estimate the accuracy of the mean eld approximation induced by the Thomas-Fermi potential for the ground state energy of atoms and molecules. Taking the Dirac exchange correction into account, we show the error to be of the form O(Z 5=3?) + D for any < 2=231 as the total nuclear charge Z becomes large. D is an electrostatic energy of the diierence… (More)