Mass Renormalization and Energy Level Shift in Non-Relativistic QED

2002/05/31 by Christian Hainzl, Robert Seiringer · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf

published as Adv. Theor. Math. Phys. 6, 847 (2002) · amslatex, 22 pages; to appear in Adv. Theor. Math. Phys

arxiv created 2003/12/27 · arxiv updated 2009/11/30

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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• The weak coupling limit of the Pauli-Fierz model

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