Reflection Structures and Spin Statistics in Low Dimensions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929441949614080 |
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| author | Müller, Lukas Stehouwer, Luuk |
| author_facet | Müller, Lukas Stehouwer, Luuk |
| contents | We give a complete classification of topological field theories with reflection structure and spin-statistics in one and two spacetime dimensions. Our answers can be naturally expressed in terms of an internal fermionic symmetry group $G$ which is different from the spacetime structure group. Fermionic groups encode symmetries of systems with fermions and time reversing symmetries. We show that 1-dimensional topological field theories with reflection structure and spin-statistics are classified by finite dimensional hermitian representations of $G$. In spacetime dimension two we give a classification in terms strongly $G$-graded stellar Frobenius algebras. Our proofs are based on the cobordism hypothesis. Along the way, we develop some useful tools for the computation of homotopy fixed points of 2-group actions on bicategories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_06664 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reflection Structures and Spin Statistics in Low Dimensions Müller, Lukas Stehouwer, Luuk Mathematical Physics Algebraic Topology Category Theory Quantum Algebra We give a complete classification of topological field theories with reflection structure and spin-statistics in one and two spacetime dimensions. Our answers can be naturally expressed in terms of an internal fermionic symmetry group $G$ which is different from the spacetime structure group. Fermionic groups encode symmetries of systems with fermions and time reversing symmetries. We show that 1-dimensional topological field theories with reflection structure and spin-statistics are classified by finite dimensional hermitian representations of $G$. In spacetime dimension two we give a classification in terms strongly $G$-graded stellar Frobenius algebras. Our proofs are based on the cobordism hypothesis. Along the way, we develop some useful tools for the computation of homotopy fixed points of 2-group actions on bicategories. |
| title | Reflection Structures and Spin Statistics in Low Dimensions |
| topic | Mathematical Physics Algebraic Topology Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2301.06664 |