A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics

Details A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics

2001-10-22

arxiv.org/abs/math-ph/0110027v4

Physics

Mathematical Physics

10 pages, LaTex. Referee comments, some stylistic changes, and some clarifying remarks at the end of Sect. 2 added. To appear

Scientific paper

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.

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