Feynman path integrals for magnetic Schrödinger operators on infinite weighted graphs
- We prove a Feynman path integral formula for the unitary group exp(-itL(nu,theta)), t >= 0, associated with a discrete magnetic Schrodinger operator L-nu,L-theta on a large class of weighted infinite graphs. As a consequence, we get a new Kato-Simon estimate vertical bar exp(- itL(nu,theta))(x,y)vertical bar <= exp( -tL(-deg,0))(x,y), which controls the unitary group uniformly in the potentials in terms of a Schrodinger semigroup, where the potential deg is the weighted degree function of the graph.
| Author details: | Batu GüneysuGND, Matthias KellerORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1007/s11854-020-0110-y |
| ISSN: | 0021-7670 |
| ISSN: | 1565-8538 |
| Title of parent work (English): | Journal d'analyse mathématique |
| Publisher: | The Magnes Press, the Hebrew Univ. |
| Place of publishing: | Jerusalem |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/08/08 |
| Publication year: | 2020 |
| Release date: | 2023/04/17 |
| Volume: | 141 |
| Issue: | 2 |
| Number of pages: | 20 |
| First page: | 751 |
| Last Page: | 770 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
