# A particle-field Hamiltonian in relativistic quantum electrodynamics

@article{Arai2000APH,
title={A particle-field Hamiltonian in relativistic quantum electrodynamics},
author={Asao Arai},
journal={Journal of Mathematical Physics},
year={2000},
volume={41},
pages={4271-4283}
}
• A. Arai
• Published 20 June 2000
• Physics
• Journal of Mathematical Physics
We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space F≔[⊕4L2(R3)]⊗Frad, where Frad is the Fock space of the quantized radiation field in the Coulomb gauge, V is an external potential in which the Dirac particle moves, g is a photon-momentum cutoff function in the interaction between the Dirac particle and the quantized radiation field, and τ∈R is a…
31 Citations
• Physics
• 2009
We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second
• Mathematics
• 2004
We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the x3‐axis and with a quantized electromagnetic field. When the interaction between the electron and
The non-relativistic (scaling) limit of a particle-field Hamiltonian H, called a Dirac–Maxwell operator, in relativistic quantum electrodynamics is considered. It is proven that the non-relativistic
In quantum field theory (QFT) models, it often seems natural to use, instead of wave functions from Fock space, wave functions that are not square-integrable and have pre-factors involving divergent
• M. Huber
• Physics
Documenta Mathematica
• 2009
This is the the second part of a series of two papers, which investigate spectral properties of Dirac operators with singular potentials. We will provide a spectral analysis of a relativistic one-
• Mathematics
• 2008
We study the Dirac operator D0 in an external potential V, coupled to a quantized radiation field with energy Hf and vector potential A. Our result is a Chernoff-type theorem, i.e., we prove, for the

## References

SHOWING 1-10 OF 15 REFERENCES

The (non-Lorentz covariant) system consisting of a relativistic scalar Boson field ϕ interacting with a single spinless particle (relativistic polaron) with kinetic energy function (m2+|p|2)1/2 is
Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Its applications are so widespread that a description of all
In 1930 Weisskopf and Wigner gave an account, based on the Maxwell–Schrodinger equations, of the natural spectral line broadening of radiation emitted by a hydrogen atom. Their calculations were
Proves that for dimensions d=1, 2 the polaron (with general dispersion relation and couplings) has a unique ground state for any value of the total momentum (particle+Bose field). For d>or=3 and for
• Physics
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
• 1951
A relativistic wave equation for helium-like systems which gives energy levels correct to within α2 Ry is derived from quantum electrodynamics, care being taken in the handling of pair-production
• Mathematics, Materials Science
• 1937
Previous methods of treating radiative corrections in non-stationary processes such as the scattering of an electron in an atomic field or the emission of a $\ensuremath{\beta}$-ray, by an expansion
In this paper the dynamics of a class of simple models (so called persistent models) including Nelson's model is studied. These models describe conserved, non relativistic, scalar electrons