A Higher Spin-Statistics Theorem for Invertible Quantum Field Theories
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916938268016640 |
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| author | Krulewski, Cameron Müller, Lukas Stehouwer, Luuk |
| author_facet | Krulewski, Cameron Müller, Lukas Stehouwer, Luuk |
| contents | We prove that every unitary invertible quantum field theory satisfies a generalization of the famous spin-statistics theorem. To formulate this extension, we define a `higher spin' action of the stable orthogonal group $O$ on appropriate spacetime manifolds, which extends both the reflection involution and spin flip. On the algebraic side, we define a `higher statistics' action of $O$ on the universal target for invertible field theories, $I\mathbb{Z}$, which extends both complex conjugation and fermion parity $(-1)^F$. We prove that every unitary invertible quantum field theory intertwines these actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Higher Spin-Statistics Theorem for Invertible Quantum Field Theories Krulewski, Cameron Müller, Lukas Stehouwer, Luuk Mathematical Physics High Energy Physics - Theory Algebraic Topology We prove that every unitary invertible quantum field theory satisfies a generalization of the famous spin-statistics theorem. To formulate this extension, we define a `higher spin' action of the stable orthogonal group $O$ on appropriate spacetime manifolds, which extends both the reflection involution and spin flip. On the algebraic side, we define a `higher statistics' action of $O$ on the universal target for invertible field theories, $I\mathbb{Z}$, which extends both complex conjugation and fermion parity $(-1)^F$. We prove that every unitary invertible quantum field theory intertwines these actions. |
| title | A Higher Spin-Statistics Theorem for Invertible Quantum Field Theories |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Topology |
| url | https://arxiv.org/abs/2408.03981 |