A Yang-Mills-Dirac Quantum Field Theory Emerging From a Dirac Operator on a Configuration Space
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917881933987840 |
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| author | Aastrup, Johannes Grimstrup, Jesper M. |
| author_facet | Aastrup, Johannes Grimstrup, Jesper M. |
| contents | Starting with a Dirac operator on a configuration space of $SU(2)$ gauge connections we consider its fluctuations with inner automorphisms. We show that a certain type of twisted inner fluctuations leads to a Dirac operator whose square gives the Hamiltonian of Yang-Mills quantum field theory coupled to a fermionic sector that consist of one-form fermions. We then show that if a metric exists on the underlying three-dimensional manifold then there exists a change of basis of the configuration space for which the transformed fermionic sector consists of fermions that are no-longer one-forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Yang-Mills-Dirac Quantum Field Theory Emerging From a Dirac Operator on a Configuration Space Aastrup, Johannes Grimstrup, Jesper M. High Energy Physics - Theory Mathematical Physics Starting with a Dirac operator on a configuration space of $SU(2)$ gauge connections we consider its fluctuations with inner automorphisms. We show that a certain type of twisted inner fluctuations leads to a Dirac operator whose square gives the Hamiltonian of Yang-Mills quantum field theory coupled to a fermionic sector that consist of one-form fermions. We then show that if a metric exists on the underlying three-dimensional manifold then there exists a change of basis of the configuration space for which the transformed fermionic sector consists of fermions that are no-longer one-forms. |
| title | A Yang-Mills-Dirac Quantum Field Theory Emerging From a Dirac Operator on a Configuration Space |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2501.00005 |