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.
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© 2003 Springer-Verlag Berlin Heidelberg
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Gustafson, S.J., Sigal, I.M. (2003). Supplement: Renormalization Group. In: Mathematical Concepts of Quantum Mechanics. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55729-3_16
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DOI: https://doi.org/10.1007/978-3-642-55729-3_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44160-1
Online ISBN: 978-3-642-55729-3
eBook Packages: Springer Book Archive