Bogoliubov Transformations Beyond Shale-Stinespring: Generic $ v^* v $ for bosons
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909719563599872 |
|---|---|
| author | Lill, Sascha |
| author_facet | Lill, Sascha |
| contents | We construct an extension of Fock space and prove that it allows for implementing bosonic Bogoliubov transformations in a certain extended sense. While an implementation in the regular sense on Fock space is only possible if a certain operator $ v^* v $ is trace class (this is the well-known Shale-Stinespring condition), the extended implementation works without any restrictions on this operator. This generalizes a recent result of extended implementability, which required $ v^* v $ to have discrete spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_03487 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bogoliubov Transformations Beyond Shale-Stinespring: Generic $ v^* v $ for bosons Lill, Sascha Mathematical Physics We construct an extension of Fock space and prove that it allows for implementing bosonic Bogoliubov transformations in a certain extended sense. While an implementation in the regular sense on Fock space is only possible if a certain operator $ v^* v $ is trace class (this is the well-known Shale-Stinespring condition), the extended implementation works without any restrictions on this operator. This generalizes a recent result of extended implementability, which required $ v^* v $ to have discrete spectrum. |
| title | Bogoliubov Transformations Beyond Shale-Stinespring: Generic $ v^* v $ for bosons |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2208.03487 |