Twisted tensor products of field algebras
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910618912555008 |
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| author | Vasselli, Ezio |
| author_facet | Vasselli, Ezio |
| contents | Let A be a C*-algebra, h a Hilbert space and C the CAR algebra over h. We construct a twisted tensor product of A by C such that the two factors are not necessarily one in the relative commutant of the other. The resulting C*-algebra may be regarded as a generalized CAR algebra constructed over a suitable Hilbert A-bimodule. As an application, we exhibit a class of fixed-time models where a free Dirac field (giving rise to the C factor) in general is not relatively local to a free scalar field (which yields the A factor). In some of the models, gauge-invariant combinations of the two (not relatively local) fields form a local observable net. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17753 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted tensor products of field algebras Vasselli, Ezio Operator Algebras Quantum Physics 46L06, 46L08, 81T05 Let A be a C*-algebra, h a Hilbert space and C the CAR algebra over h. We construct a twisted tensor product of A by C such that the two factors are not necessarily one in the relative commutant of the other. The resulting C*-algebra may be regarded as a generalized CAR algebra constructed over a suitable Hilbert A-bimodule. As an application, we exhibit a class of fixed-time models where a free Dirac field (giving rise to the C factor) in general is not relatively local to a free scalar field (which yields the A factor). In some of the models, gauge-invariant combinations of the two (not relatively local) fields form a local observable net. |
| title | Twisted tensor products of field algebras |
| topic | Operator Algebras Quantum Physics 46L06, 46L08, 81T05 |
| url | https://arxiv.org/abs/2401.17753 |