Volker Bach, Thomas Chen, Juerg Froehlich, Israel Michael Sigal
Smooth Feshbach Map and Operator-Theoretic Renormalization Group Methods
(452K, Postscript)

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.