Elementary commutator method for the Dirac equation with long-range perturbations
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915783322370048 |
|---|---|
| author | Arita, Shinichi Ito, Kenichi |
| author_facet | Arita, Shinichi Ito, Kenichi |
| contents | We present direct and elementary commutator techniques for the Dirac equation with long-range electric and mass perturbations. The main results are absence of generalized eigenfunctions and locally uniform resolvent estimates, both in terms of the optimal Besov-type spaces. With an additional massless assumption, we also obtain an algebraic radiation condition of projection type. For their proofs, following the scheme of Ito-Skibsted, we adopt, along with various weight functions, the generator of radial translations as conjugate operator, and avoid any of advanced functional analysis, pseudodifferential calculus, or even reduction to the Schrödinger equation. The results of the paper would serve as a foundation for the stationary scattering theory of the Dirac operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08209 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elementary commutator method for the Dirac equation with long-range perturbations Arita, Shinichi Ito, Kenichi Mathematical Physics Analysis of PDEs Functional Analysis Spectral Theory We present direct and elementary commutator techniques for the Dirac equation with long-range electric and mass perturbations. The main results are absence of generalized eigenfunctions and locally uniform resolvent estimates, both in terms of the optimal Besov-type spaces. With an additional massless assumption, we also obtain an algebraic radiation condition of projection type. For their proofs, following the scheme of Ito-Skibsted, we adopt, along with various weight functions, the generator of radial translations as conjugate operator, and avoid any of advanced functional analysis, pseudodifferential calculus, or even reduction to the Schrödinger equation. The results of the paper would serve as a foundation for the stationary scattering theory of the Dirac operator. |
| title | Elementary commutator method for the Dirac equation with long-range perturbations |
| topic | Mathematical Physics Analysis of PDEs Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2511.08209 |