221 citations · 439 across the 29 of their papers we have counts for
33 papers
Bounds on the Bogoliubov--Hartree--Fock Energy of the Pauli--Fierz Hamiltonian
Volker Bach, Matthias Herdzik
A variational analysis of the Bogoliubov--Hartree--Fock (BHF) energy of the translation-invariant, spinless Pauli--Fierz Hamiltonian with massless dispersion relation built up on w…
On the Ultraviolet Problem for the Ground State Energy of the Translation-Invariant Pauli--Fierz Model at Zero Total Momentum
Volker Bach, Miguel Ballesteros, Merten Mlinarzik
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 t…
The Birman--Solomyak theorem revisited: a novel elementary proof, generalisation, and applications
V. Bach, A. F. M. ter Elst, J. Rehberg
We provide a new short proof for the Birman--Solomyak theorem for Hilbert--Schmidt operators and give an application to a Schrödinger--Poisson system.
The Spectral Renormalization Flow Based on the Smooth Feshbach--Schur Map: The Introduction of the Semi-Group Property
Volker Bach, Miguel Ballesteros, Jakob Geisler
The spectral renormalization method is a powerful mathematical tool that is prominently used in spectral theory in the context of low-energy quantum field theory and its original i…
On Relative Bounds for Interacting Fermion Operators
Volker Bach, Robert Rauch
We consider a Hubbard model with nearest neighbor interaction on a discrete -dimensional torus of length around its Hartree-Fock ground state and derive relative bounds of t…
Hartree--Fock Theory, Lieb's Variational Principle, and their Generalizations
Volker Bach
Hartree--Fock theory in quantum mechanics is reviewed, from the proposal of the Hartree--Fock approximation right after quantum mechanics was formulated to its applications in mode…