Fermionic renormalization group method based on the smooth Feshbach map

with d ∈ N and s a non-negative half integer, and denote the creation and annihilation operators by b∗(k), b(k), which formally obey the canonical anticommutation relations, {b(k), b∗(k̃)} = δl,l̃δ(k− k̃), {b(k), b(k̃)} = {b ∗(k), b∗(k̃)} = 0, k = (k, l), k = (k̃, l̃) ∈ M ≡ R × L. If the Hamiltonian HS has a discrete eigenvalue E the free Hamiltonian H0 of the total system has the same eigenvalue E, which is an embedded eigenvalue because the spectrum of Hf is equal to [0,∞). We discuss the fate of the eigenvalue E when the perturbation Wg is swiched on by using the operator theoretic renormalization group method based on the smooth Feshbach map, which is introduced by V. Bach, T. Chen, J. Fröhlich and I. M. Sigal. ∗This work was supported by Japan Society for the Promotion of Science (JSPS). †This work was supported by Japan Society for the Promotion of Science (JSPS).