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Annales Henri Poincaré

, Volume 10, Issue 3, pp 577–621 | Cite as

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

  • Marcel GriesemerEmail author
  • David G. Hasler
Article

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.

Keywords

Ground State Energy Dipole Approximation Analytic Family Analytic Perturbation Theory Adiabatic Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

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

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