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Supplement: Renormalization Group

  • Stephen J. Gustafson
  • Israel Michael Sigal
Part of the Universitext book series (UTX)

Abstract

In this chapter we describe an operator version of the renormalization group method, due to [BFS1]-[BFS4]_(see also [GaW, Weg, KM]). We demonstrate how this method works by applying it to the problem of radiation described in Chapter 15. In particular, we continue our study of the Hamiltonian H (ε) which describes quantum particles coupled to the quantized EM field. We outline a proof of part (i) of Theorem 15.2, which states the existence of the ground state of the operator H(ε) for sufficiently small |ε|. The problems of instability of the excited states and existence of the resonances — statements (ii) and (iii) of Theorem 15.2 — can be treated in the same way.

Keywords

Banach Space Renormalization Group Ground State Energy Stable Manifold Coupling Function 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Stephen J. Gustafson
    • 1
  • Israel Michael Sigal
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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