Bogoliubov Transformations Beyond Shale-Stinespring: Generic $ v^* v $ for bosons
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909719563599872 |
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| 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 |