Supplement: Renormalization Group
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.
KeywordsBanach Space Renormalization Group Ground State Energy Stable Manifold Coupling Function
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