 01417 Elliott H. Lieb, Michael Loss
 A Bound on Binding Energies and Mass Renormalization
in Models of Quantum Electrodynamics
(34K, Latex, 10 pages)
Nov 8, 01

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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 PauliFierz
energy (p+eA(x))^2 +e\sigma \cdot B(x). The third, nopair 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.
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