Elliott H. Lieb, Michael Loss
A Bound on Binding Energies and Mass Renormalization 
in Models of Quantum Electrodynamics
(34K, Latex, 10 pages)

ABSTRACT.  We study three well known models of matter coupled to the ultraviolet 
cutoff, quantized radiation field and to the Coulomb potential of 
arbitrarily many nuclei. Two are nonrelativistic: the first uses 
the kinetic energy (p+eA(x))^2 and the second uses the Pauli-Fierz 
energy (p+eA(x))^2 +e\sigma \cdot B(x). The third, no-pair model, is 
relativistic and replaces the kinetic energy with the Dirac operator 
D(A), but restricted to its positive spectral subspace, which is the 
``electron subspace". In each case we are able to give an upper bound to 
the {\it binding} energy -- as distinct from the less difficult ground 
state energy. This implies, for the first time we believe, an estimate, 
albeit a crude one, of the mass renormalization in these theories.