Annales Henri Poincaré

, Volume 10, Issue 3, pp 577–621

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

Article

DOI: 10.1007/s00023-009-0417-9

Cite this article as:
Griesemer, M. & Hasler, D.G. Ann. Henri Poincaré (2009) 10: 577. doi:10.1007/s00023-009-0417-9

Abstract.

For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of α3/2, α being the fine structure constant. A suitably chosen ground state vector depends analytically on α3/2 and it is twice continuously differentiable with respect to the nuclear coordinates.

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© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität StuttgartStuttgartGermany
  2. 2.Department of MathematicsCollege of William & MaryWilliamsburgUSA