2024-03-28T12:18:11Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696582022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Fermionic renormalization group method based on the smooth Feshbach mapSasaki, ItaruSuzuki, Akitoopen accesssmooth Feshbach maprenormalization groupfermionic renormalization group410For a fermion system, an operator theoretic renormalization group method based on the smooth Feshbach map is constructed. By using the fermionic renormalization group method, the closed operator of the form: Hg(θ) = HS ⊗ 1 + eθν1 ⊗ Hf + Wg(θ) is analyzed, where HS is a selfadjoint operator on a separable Hilbert space and bounded from below, Hf denotes the fermionic quantization of the one fermion kinetic energy c|k|ν, k ∈ Rd (c, ν > 0), Wg(θ) is a small perturbation with respect to HS ⊗ 1 + eθν1 ⊗ Hf and θ ∈ C is a complex scaling parameter. The constant g ∈ R denotes a coupling constant such that Wg(θ) → 0(g → 0) in some sense. It is assumed that HS has a discrete simple eigenvalue E ∈ σd(HS), and proved that Hg(θ) has an eigenvalue Eg(θ) close to E for a small coupling constant g. Moreover, the eigenvalue Eg(θ) and the corresponding eigenvector Ψ(θ) is constructed by the process of the operator theoretic renormalization group method.Department of Mathematics, Hokkaido University2007-05-09engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83999http://hdl.handle.net/2115/6965810.14943/83999Hokkaido University Preprint Series in Mathematics849135https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69658/1/pre849.pdfapplication/pdf232.93 KB2007-05-09