Annales Henri Poincaré

, Volume 15, Issue 5, pp 863–915 | Cite as

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

Article

Abstract

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 \({\mathfrak{p} > 0}\), provided that the coupling constant is sufficiently small depending on \({\mathfrak{p}}\) 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.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Fakultät für PhysikUniversität WienViennaAustria
  2. 2.Mathematisches InstitutLudwig-Maximilians-UniversitätMünchenGermany
  3. 3.Institut for MatematikÅrhus UniversitetÅrhus CDenmark

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