The Hermitian axiom on two-dimensional topological quantum field theories
We examine Atiyah’s Hermitian axiom for two-dimensional complex topological quantum field theories. Building on the correspondence between 2D topological quantum field theories (TQFTs) and Frobenius algebras, we find the algebraic objects corresponding to Hermitian and unitary TQFTs, respectively, a...
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| Format: | Article |
| Language: | en_US |
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AIP Publishing
2023
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| Online Access: | https://hdl.handle.net/1721.1/153229 |
| _version_ | 1811085398976233472 |
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| author | Zhu, Honglin |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Zhu, Honglin |
| author_sort | Zhu, Honglin |
| collection | MIT |
| description | We examine Atiyah’s Hermitian axiom for two-dimensional complex topological quantum field theories. Building on the correspondence between 2D topological quantum field theories (TQFTs) and Frobenius algebras, we find the algebraic objects corresponding to Hermitian and unitary TQFTs, respectively, and prove structure theorems about them. We then clarify a few older results on unitary TQFTs using our structure theorems. |
| first_indexed | 2024-09-23T13:08:57Z |
| format | Article |
| id | mit-1721.1/153229 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:08:57Z |
| publishDate | 2023 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1532292024-01-05T16:12:30Z The Hermitian axiom on two-dimensional topological quantum field theories Zhu, Honglin Massachusetts Institute of Technology. Department of Mathematics Mathematical Physics Statistical and Nonlinear Physics We examine Atiyah’s Hermitian axiom for two-dimensional complex topological quantum field theories. Building on the correspondence between 2D topological quantum field theories (TQFTs) and Frobenius algebras, we find the algebraic objects corresponding to Hermitian and unitary TQFTs, respectively, and prove structure theorems about them. We then clarify a few older results on unitary TQFTs using our structure theorems. 2023-12-21T21:19:25Z 2023-12-21T21:19:25Z 2023-02-01 Article http://purl.org/eprint/type/JournalArticle 0022-2488 1089-7658 https://hdl.handle.net/1721.1/153229 Honglin Zhu; The Hermitian axiom on two-dimensional topological quantum field theories. J. Math. Phys. 1 February 2023; 64 (2): 022301. en_US 10.1063/5.0121440 Journal of Mathematical Physics Creative Commons Attribution An error occurred on the license name. https://creativecommons.org/licenses/by/4.0/ application/pdf AIP Publishing AIP Publishing |
| spellingShingle | Mathematical Physics Statistical and Nonlinear Physics Zhu, Honglin The Hermitian axiom on two-dimensional topological quantum field theories |
| title | The Hermitian axiom on two-dimensional topological quantum field theories |
| title_full | The Hermitian axiom on two-dimensional topological quantum field theories |
| title_fullStr | The Hermitian axiom on two-dimensional topological quantum field theories |
| title_full_unstemmed | The Hermitian axiom on two-dimensional topological quantum field theories |
| title_short | The Hermitian axiom on two-dimensional topological quantum field theories |
| title_sort | hermitian axiom on two dimensional topological quantum field theories |
| topic | Mathematical Physics Statistical and Nonlinear Physics |
| url | https://hdl.handle.net/1721.1/153229 |
| work_keys_str_mv | AT zhuhonglin thehermitianaxiomontwodimensionaltopologicalquantumfieldtheories AT zhuhonglin hermitianaxiomontwodimensionaltopologicalquantumfieldtheories |