# Mass renormalization and energy level shift in non-relativistic QED

Hainzl C, Seiringer R. 2002. Mass renormalization and energy level shift in non-relativistic QED. Advances in Theoretical and Mathematical Physics. 6(5), 847–871.

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Author

Hainzl, Christian;
Seiringer, Robert

^{ISTA}^{}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.

Publishing Year

Date Published

2002-09-01

Journal Title

Advances in Theoretical and Mathematical Physics

Volume

6

Issue

5

Page

847 - 871

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### Cite this

Hainzl C, Seiringer R. Mass renormalization and energy level shift in non-relativistic QED.

*Advances in Theoretical and Mathematical Physics*. 2002;6(5):847-871.Hainzl, C., & Seiringer, R. (2002). Mass renormalization and energy level shift in non-relativistic QED.

*Advances in Theoretical and Mathematical Physics*. International Press.Hainzl, Christian, and Robert Seiringer. “Mass Renormalization and Energy Level Shift in Non-Relativistic QED.”

*Advances in Theoretical and Mathematical Physics*. International Press, 2002.C. Hainzl and R. Seiringer, “Mass renormalization and energy level shift in non-relativistic QED,”

*Advances in Theoretical and Mathematical Physics*, vol. 6, no. 5. International Press, pp. 847–871, 2002.Hainzl, Christian, and Robert Seiringer. “Mass Renormalization and Energy Level Shift in Non-Relativistic QED.”

*Advances in Theoretical and Mathematical Physics*, vol. 6, no. 5, International Press, 2002, pp. 847–71.**All files available under the following license(s):**

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