Dirac Operators on Configuration Spaces and Yang-Mills Quantum Field Theory
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914975410290688 |
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| author | Aastrup, Johannes Grimstrup, Jesper M. |
| author_facet | Aastrup, Johannes Grimstrup, Jesper M. |
| contents | In this paper we discuss a connection between Dirac operators on configuration spaces and Yang-Mills quantum field theory. We first show that the Hamilton operators of the self-dual and anti-self-dual sectors of a Yang-Mills quantum field theory emerge from unitary transformations of a Dirac equation formulated on a configuration space of gauge connections. Secondly, we formulate a Bott-Dirac operator on the configuration space and demonstrate how the Hamilton operator of a Yang-Mills quantum field theory coupled to a fermionic sector emerges from its square. Finally, we discuss a spectral invariant that emerges in this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirac Operators on Configuration Spaces and Yang-Mills Quantum Field Theory Aastrup, Johannes Grimstrup, Jesper M. High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics In this paper we discuss a connection between Dirac operators on configuration spaces and Yang-Mills quantum field theory. We first show that the Hamilton operators of the self-dual and anti-self-dual sectors of a Yang-Mills quantum field theory emerge from unitary transformations of a Dirac equation formulated on a configuration space of gauge connections. Secondly, we formulate a Bott-Dirac operator on the configuration space and demonstrate how the Hamilton operator of a Yang-Mills quantum field theory coupled to a fermionic sector emerges from its square. Finally, we discuss a spectral invariant that emerges in this framework. |
| title | Dirac Operators on Configuration Spaces and Yang-Mills Quantum Field Theory |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2410.03699 |