Dirac Operators on Configuration Spaces: Fermions with Half-integer Spin, Real Structure, and Yang-Mills Quantum Field Theory
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913549853392896 |
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| author | Aastrup, Johannes Grimstrup, Jesper M. |
| author_facet | Aastrup, Johannes Grimstrup, Jesper M. |
| contents | In this paper we continue the development of a spectral triple-like construction on a configuration space of gauge connections. We have previously shown that key elements of bosonic and fermionic quantum field theory emerge from such a geometrical framework. In this paper we solve a central problem concerning the inclusion of fermions with half-integer spin into this framework. We map the tangent space of the configuration space into a similar space based on spinors and use this map to construct a Dirac operator on the configuration space. We also construct a real structure acting in a Hilbert space over the configuration space. Finally, we show that the self-dual and anti-self-dual sectors of the Hamiltonian of a non-perturbative quantum Yang-Mills theory emerge from a unitary transformation of a Dirac equation on a configuration space of gauge fields. The dual and anti-dual sectors emerge in a two-by-two matrix structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07290 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirac Operators on Configuration Spaces: Fermions with Half-integer Spin, Real Structure, and Yang-Mills Quantum Field Theory Aastrup, Johannes Grimstrup, Jesper M. Mathematical Physics High Energy Physics - Theory In this paper we continue the development of a spectral triple-like construction on a configuration space of gauge connections. We have previously shown that key elements of bosonic and fermionic quantum field theory emerge from such a geometrical framework. In this paper we solve a central problem concerning the inclusion of fermions with half-integer spin into this framework. We map the tangent space of the configuration space into a similar space based on spinors and use this map to construct a Dirac operator on the configuration space. We also construct a real structure acting in a Hilbert space over the configuration space. Finally, we show that the self-dual and anti-self-dual sectors of the Hamiltonian of a non-perturbative quantum Yang-Mills theory emerge from a unitary transformation of a Dirac equation on a configuration space of gauge fields. The dual and anti-dual sectors emerge in a two-by-two matrix structure. |
| title | Dirac Operators on Configuration Spaces: Fermions with Half-integer Spin, Real Structure, and Yang-Mills Quantum Field Theory |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.07290 |