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Fermionic renormalization group method based on the smooth Feshbach map
| Title: | Fermionic renormalization group method based on the smooth Feshbach map |
| Authors: | Sasaki, Itaru Browse this author | | Suzuki, Akito Browse this author |
| Keywords: | smooth Feshbach map | | renormalization group | | fermionic renormalization group |
| Issue Date: | 9-May-2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 849 |
| Start Page: | 1 |
| End Page: | 35 |
| Abstract: | For 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69658 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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