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

TL;DR

This paper establishes upper bounds on binding energies in various quantum electrodynamics models with ultraviolet cutoff, providing initial estimates for mass renormalization in these theories.

Contribution

It introduces the first known bounds on binding energies in multiple QED models, offering crude estimates for mass renormalization.

Findings

Upper bounds on binding energies derived for three QED models.

First estimates of mass renormalization in these models.

Applicable to both nonrelativistic and relativistic frameworks.

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.