Undecidable problems in quantum field theory
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929599267471360 |
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| author | Tachikawa, Yuji |
| author_facet | Tachikawa, Yuji |
| contents | We point out that some questions in quantum field theory are undecidable in a precise mathematical sense. More concretely, it will be demonstrated that there is no algorithm answering whether a given 2d supersymmetric Lagrangian theory breaks supersymmetry or not. It will also be shown that there is a specific 2d supersymmetric Lagrangian theory which breaks supersymmetry if and only if the standard Zermelo-Fraenkel set theory with the axiom of choice is consistent, which can never be proved or disproved as the consequence of Gödel's second incompleteness theorem. The article includes a brief and informal introduction to the phenomenon of undecidability and its previous appearances in theoretical physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_16689 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Undecidable problems in quantum field theory Tachikawa, Yuji High Energy Physics - Theory We point out that some questions in quantum field theory are undecidable in a precise mathematical sense. More concretely, it will be demonstrated that there is no algorithm answering whether a given 2d supersymmetric Lagrangian theory breaks supersymmetry or not. It will also be shown that there is a specific 2d supersymmetric Lagrangian theory which breaks supersymmetry if and only if the standard Zermelo-Fraenkel set theory with the axiom of choice is consistent, which can never be proved or disproved as the consequence of Gödel's second incompleteness theorem. The article includes a brief and informal introduction to the phenomenon of undecidability and its previous appearances in theoretical physics. |
| title | Undecidable problems in quantum field theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2203.16689 |