Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.07643 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915438265368576 |
|---|---|
| author | Bach, Volker Ballesteros, Miguel Geisler, Jakob |
| author_facet | Bach, Volker Ballesteros, Miguel Geisler, Jakob |
| contents | The spectral renormalization method is a powerful mathematical tool that is prominently used in spectral theory in the context of low-energy quantum field theory and its original introduction in [5, 6] constituted a milestone in the field. Inspired by physics, this method is usually called renormalization group, even though it is not a group nor a semigroup (or, more properly, a flow). It was only in 2015 in [1] when a flow (or semigroup) structure was first introduced using an innovative definition of the renormalization of spectral parameters. The spectral renormalization flow in [1], however, is not compatible with the smooth Feshbach--Schur map (this is stated as an open problem in [1]), which is a lamentable weakness because its smoothness is a key feature that significantly simplifies the proofs and makes it the preferred tool in most of the literature. In this paper we solve this open problem introducing a spectral renormalization flow based on the smooth Feshbach--Schur map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Spectral Renormalization Flow Based on the Smooth Feshbach--Schur Map: The Introduction of the Semi-Group Property Bach, Volker Ballesteros, Miguel Geisler, Jakob Mathematical Physics 81T16, 81T17 The spectral renormalization method is a powerful mathematical tool that is prominently used in spectral theory in the context of low-energy quantum field theory and its original introduction in [5, 6] constituted a milestone in the field. Inspired by physics, this method is usually called renormalization group, even though it is not a group nor a semigroup (or, more properly, a flow). It was only in 2015 in [1] when a flow (or semigroup) structure was first introduced using an innovative definition of the renormalization of spectral parameters. The spectral renormalization flow in [1], however, is not compatible with the smooth Feshbach--Schur map (this is stated as an open problem in [1]), which is a lamentable weakness because its smoothness is a key feature that significantly simplifies the proofs and makes it the preferred tool in most of the literature. In this paper we solve this open problem introducing a spectral renormalization flow based on the smooth Feshbach--Schur map. |
| title | The Spectral Renormalization Flow Based on the Smooth Feshbach--Schur Map: The Introduction of the Semi-Group Property |
| topic | Mathematical Physics 81T16, 81T17 |
| url | https://arxiv.org/abs/2508.07643 |