Smooth Feshbach map and operator-theoretic renormalization group methods |
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Authors: | Volker Bach,Thomas Chen,Jü rg Frö hlich,Israel Michael Sigal |
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Affiliation: | a FB Mathematik, Universität Mainz, D-55099 Mainz, Germany b Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, USA c Inst. f. Theoretische Physik, ETH Hönggerberg, CH-8093 Zürich, Switzerland d Department of Mathematics, University of Toronto, Toronto, Canada M5S 3G3 |
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Abstract: | A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map. It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel operator-theoretic renormalization group method is described and applied to analyze a general class of Hamiltonians on Fock space. The main advantage of the new renormalization group method over its predecessors is its technical simplicity, which it owes to the use of the smooth Feshbach map. |
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