An entropy bound due to symmetries
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911748157603840 |
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| author | Longo, Roberto Morinelli, Vincenzo |
| author_facet | Longo, Roberto Morinelli, Vincenzo |
| contents | Let $H$ be a local net of real Hilbert subspaces of a complex Hilbert space on the family of double cones of the spacetime $\mathbb{R}^{d+1}$, covariant with respect to a positive energy, unitary representation $U$ of the Poincaré group, with the Bisognano-Wichmann property for the wedge modular group. We set an upper bound on the local entropy $S_H(ϕ|\! | C)$ of a vector in a region $C$ that depends only on $U$ and the PCT anti-unitary canonically associated with $H$. A similar result holds for local, Möbius covariant nets of standard subspaces on the circle. We compute the entropy increase and illustrate this bound for the nets associated with the $U(1)$-current derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An entropy bound due to symmetries Longo, Roberto Morinelli, Vincenzo Operator Algebras High Energy Physics - Theory Mathematical Physics 81T05, 81P45, 94A17, 46L60, 81T40 Let $H$ be a local net of real Hilbert subspaces of a complex Hilbert space on the family of double cones of the spacetime $\mathbb{R}^{d+1}$, covariant with respect to a positive energy, unitary representation $U$ of the Poincaré group, with the Bisognano-Wichmann property for the wedge modular group. We set an upper bound on the local entropy $S_H(ϕ|\! | C)$ of a vector in a region $C$ that depends only on $U$ and the PCT anti-unitary canonically associated with $H$. A similar result holds for local, Möbius covariant nets of standard subspaces on the circle. We compute the entropy increase and illustrate this bound for the nets associated with the $U(1)$-current derivatives. |
| title | An entropy bound due to symmetries |
| topic | Operator Algebras High Energy Physics - Theory Mathematical Physics 81T05, 81P45, 94A17, 46L60, 81T40 |
| url | https://arxiv.org/abs/2401.02345 |