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The Mass Shell in the Semi-Relativistic Pauli-Fierz Model

Autor(en)

Martin Koenenberg, Oliver Matte

Abstrakt

We consider the semi-relativistic Pauli–Fierz model for a single free

electron interacting with the quantized radiation field. Employing a

variant of Pizzo’s iterative analytic perturbation theory we construct a

sequence of ground state eigenprojections of infra-red cutoff, dressing

transformed fiber Hamiltonians and prove its convergence, as the cutoff

goes to zero. Its limit is the ground state eigenprojection of a

certain renormalized fiber Hamiltonian. The ground state energy is an

exactly twofold degenerate eigenvalue of the renormalized Hamiltonian,

while it is not an eigenvalue of the original fiber Hamiltonian unless

the total momentum is zero. These results hold true, for total momenta

inside a ball about zero of arbitrary radius p>0 , provided that the coupling constant is sufficiently small depending on p

and the ultra-violet cutoff. Along the way we prove twice continuous

differentiability and strict convexity of the ground state energy as a

function of the total momentum inside that ball.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Ludwig-Maximilians-Universität München

Journal

Annales Henri Poincare

Band

Seiten

863-915

Anzahl der Seiten

ISSN

1424-0637

DOI

https://doi.org/10.1007/s00023-013-0268-2

Publikationsdatum

05-2014

Peer-reviewed

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Nuclear and High Energy Physics, Statistical and Nonlinear Physics, Mathematical Physics

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