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Mass Renormalization and Energy Level Shift in Non-Relativistic QED

Christian Hainzl·Robert Seiringer
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Abstract

Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge $Z$ and in presence of the quantized radiation field. We consider the case of small coupling constant $α$, but fixed $Zα$ and ultraviolet cut-off $Λ$. We prove that after renormalizing the mass the binding energy has, to leading order in $α$, a finite limit as $Λ$ goes to infinity; i.e., the cut-off can be removed. The expression for the ground state energy shift thus obtained agrees with Bethe's formula for small values of $Zα$, but shows a different behavior for bigger values.

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Christian Hainzl, Robert Seiringer. 2003-12-27. Mass Renormalization and Energy Level Shift in Non-Relativistic QED. https://arxiv.org/abs/math-ph/0205044

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