6533b7d1fe1ef96bd125baef
RESEARCH PRODUCT
Smooth Feshbach map and operator-theoretic renormalization group methods
Thomas ChenJürg FröhlichVolker BachIsrael Michael Sigalsubject
Singular perturbationClass (set theory)010102 general mathematicsMathematical analysisHilbert spaceRenormalization group01 natural sciencesFock spacesymbols.namesakeIsospectralPartition of unity0103 physical sciencessymbolsFunctional renormalization group010307 mathematical physics0101 mathematicsAnalysisMathematical physicsMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-09-01 | Journal of Functional Analysis |