81 research outputs found
Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics
Starting from a formal Hamiltonian as found in the physics literature --
omitting photons -- we define a renormalized Hamiltonian through charge and
mass renormalization. We show that the restriction to the one-electron subspace
is well-defined. Our construction is non-perturbative and does not use a
cut-off. The Hamiltonian is relevant for the description of the Lamb shift in
muonic atoms.Comment: Reformulation of main theorem, minor changes in the proo
The Atomic Density on the Thomas--Fermi Length Scale for the Chandrasekhar Hamiltonian
We consider a large neutral atom of atomic number , modeled by a
pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably
rescaled one-particle ground state density on the Thomas--Fermi length scale
. Using an observation by Fefferman and Seco (1989), we find that the
density on this scale converges to the minimizer of the Thomas--Fermi
functional of hydrogen as when is fixed to a value not
exceeding . This shows that the electron density on the Thomas--Fermi
length scale does not exhibit any relativistic effects
THE GROUND STATE ENERGY OF HEAVY ATOMS (Tosio Kato Centennial Conference)
We review results on the asymptotic behavior of the groundstate energy and the reduced one-particle ground state density of large atoms
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