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Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics

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Abstract

Starting from a formal Hamiltonian as found in the physics literature – omitting photons – we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction to the one-electron subspace is well-defined. Our construction is non-perturbative and does not use a cut-off. The Hamiltonian is relevant for the description of the Lamb shift in muonic atoms.

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  1. Mathematik, Theresienstrasse 39, 80333, München, Germany

    Christian Hainzl & Heinz Siedentop

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  1. Christian Hainzl
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  2. Heinz Siedentop
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Correspondence to Heinz Siedentop.

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Communicated by B. Simon

C.H. has been supported by a Marie Curie Fellowship of the European Community program ‘‘Improving Human Research Potential and the Socio-economic Knowledge Base’’ under contract number HPMFCT-2000-00660. Both authors acknowledge partial support through the European Union’s IHP network Analysis & Quantum HPRN-CT-2002-00277

© 2003 The authors. Reproduction of this article for non-commercial purposes by any means is permitted.

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Hainzl, C., Siedentop, H. Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics. Commun. Math. Phys. 243, 241–260 (2003). https://doi.org/10.1007/s00220-003-0958-6

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