Proceedings of the American Mathematical Society

Author(s): Jean-Marie Barbaroux; Thomas Chen; Vitali Vougalter; Semjon Vugalter
Journal: Proc. Amer. Math. Soc. 136 (2008), 1057-1064.
MSC (2000): Primary 81Q10
Posted: November 23, 2007
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Abstract: In this note, we determine the ground state energy of the translation invariant Pauli-Fierz model to subleading order $O(\alpha^3)$ with respect to powers of the finestructure constant $\alpha$ and prove rigorous error bounds of order $O(\alpha^{4})$ . A main objective of our argument is its brevity.

1.: V. Bach, T. Chen, J. Fröhlich, I.M. Sigal, The renormalized electron mass in non-relativistic quantum electrodynamics. J. Funct. Anal., 243 (2), 426-535, 2007. MR 2289695
2.: J.-M. Barbaroux, T. Chen, S.A. Vugalter, Binding conditions for atomic -electron systems in non-relativistic QED, Ann. Henri Poincaré, 4, 1101-1136, 2003. MR 2031161 (2005g:81348)
3.: V. Bach, J. Fröhlich, A. Pizzo, Infrared-finite algorithms in QED: The groundstate of an atom interacting with the quantized radiation field, Comm. Math. Phys., 264 (1), 145-165, 2006. MR 2212219 (2007d:81248)
4.: I. Catto, C. Hainzl, Self-energy of one electron in non-relativistic QED, J. Funct. Anal., 207, 68-110, 2004. MR 2027637 (2005f:81294)
5.: T. Chen, Infrared renormalization in non-relativistic QED and scaling criticality, submitted (preprint http://arxiv.org/abs/math-ph/0601010), 2006.
6.: T. Chen, J. Fröhlich, Coherent infrared representations in non-relativistic QED, Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday, Proc. Sympos. Pure Math., AMS, 2007. (preprint http://xxx.arxiv.org/abs/math-ph/0601009). MR 2310197
7.: C. Hainzl, M. Hirokawa, H. Spohn, Binding energy for hydrogen-like atoms in the Nelson model without cutoffs. J. Funct. Anal., 220 (2), 424-459, 2005. MR 2119286 (2005k:81362)
8.: C. Hainzl, V. Vougalter, S.A. Vugalter, Enhanced binding in non-relativistic QED, Comm. Math. Phys., 233, 13-26, 2003. MR 1957730 (2003j:81247)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 81Q10

Jean-Marie Barbaroux
Affiliation: Centre de Physique Théorique, Luminy Case 907, 13288 Marseille Cedex~9, France, and Département de Mathématiques, Université du Sud Toulon-Var, 83957 La Garde Cedex, France
Email: barbarou@univ-tln.fr

Thomas Chen
Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544
Email: tc@math.princeton.edu

Vitali Vougalter
Affiliation: Mathematics Department, 202 Mathematical Sciences Bldg, University of Missouri, Columbia, Missouri 65211-4100
Email: vitali@math.missouri.edu

Semjon Vugalter
Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresien- strasse 39, 80333 München, and Institut für Analysis, Dynamik und Modellierung, Universität Stuttgart
Email: wugalter@mathematik.uni-muenchen.de

DOI: 10.1090/S0002-9939-07-09241-6
PII: S 0002-9939(07)09241-6
Received by editor(s): December 29, 2006
Posted: November 23, 2007
Communicated by: Michael I. Weinstein
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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