On the Ultraviolet Limit of the Pauli–Fierz Hamiltonian in the Lieb–Loss Model

@article{Bach2022OnTU,
  title={On the Ultraviolet Limit of the Pauli–Fierz Hamiltonian in the Lieb–Loss Model},
  author={Volker Bach and Alexander Hach},
  journal={Annales Henri Poincar{\'e}},
  year={2022}
}
  • V. Bach, A. Hach
  • Published 14 April 2020
  • Chemistry, Physics, Art, Computer Science
  • Annales Henri Poincaré
<jats:p>Two decades ago, Lieb and Loss (Self-energy of electrons in non-perturbative QED. Preprint <jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="http://arxiv.org/abs/math-ph/9908020">arXiv:math-ph/9908020</jats:ext-link> and mp-arc #99–305, 1999) approximated the ground state energy of a free, nonrelativistic electron coupled to the quantized radiation field by the infimum <jats:inline-formula><jats:alternatives><jats:tex-math>$$E_{\alpha , \Lambda… 
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References

SHOWING 1-10 OF 38 REFERENCES
Derivation of the magnetic Euler–Heisenberg energy
Spectral Theory of the Fermi Polaron
The Fermi polaron refers to a system of free fermions interacting with an impurity particle by means of two-body contact forces. Motivated by the physicists’ approach to this system, the present
Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms
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
Minimization of the Energy of the Non-Relativistic One-Electron Pauli-Fierz Model over Quasifree States
In this article the existence of a minimizer for the energy for the nonrelativistic one-electron Pauli-Fierz model wi thin the class of quasifree states is established. To this end it is shown that
Quantum Electrodynamics. I. A Covariant Formulation
Attempts to avoid the divergence difficulties of quantum electrodynamics by multilation of the theory have been uniformly unsuccessful. The lack of convergence does indicate that a revision of
The mean‐field approximation in quantum electrodynamics: The no‐photon case
We study the mean‐field approximation of quantum electrodynamics (QED) by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normal ordering or
Infrared-Finite Algorithms in QED: The Groundstate of an Atom Interacting with the Quantized Radiation Field
In this paper, the groundstate of a nonrelativistic atom, minimally coupled to the quantized radiation field, and its groundstate energy are constructed by an iteration scheme inspired by [10]. This
Space - time approach to quantum electrodynamics
In this paper two things are done. (1) It is shown that a considerable simplification can be attained in writing down matrix elements for complex processes in electrodynamics. Further, a physical
Generalized Hartree-Fock theory and the Hubbard model
The familiar unrestricted Hartree-Fock variational principles is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matrices
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