Global Gauge Symmetries and Spatial Asymptotic Boundary Conditions in Yang-Mills theory
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910136802476032 |
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| author | Borsboom, Silvester Posthuma, Hessel |
| author_facet | Borsboom, Silvester Posthuma, Hessel |
| contents | In Yang-Mills theory on a Euclidean Cauchy surface, the physical gauge group is often taken to be $\mathcal{G}^I/\mathcal{G}^\infty_0$, where $\mathcal{G}^I$ consists of boundary-preserving gauge transformations asymptoting to a constant, and $\mathcal{G}^\infty_0$ consists of transformations generated by the Gauss law constraint. We rigorously derive this physical gauge group for both Abelian and non-Abelian theories. A key result is that restricting to $\mathcal{G}^I$ follows from the structure of the instantaneous state space on which the instantaneous Lagrangian is defined. We extend our analysis to Yang-Mills-Higgs theory, showing that boundary conditions and the physical gauge group differ between the unbroken and broken phases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_16151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Gauge Symmetries and Spatial Asymptotic Boundary Conditions in Yang-Mills theory Borsboom, Silvester Posthuma, Hessel Mathematical Physics High Energy Physics - Theory History and Philosophy of Physics 70S15 (Primary) 70S05, 70S10, 53D20 (Secondary) In Yang-Mills theory on a Euclidean Cauchy surface, the physical gauge group is often taken to be $\mathcal{G}^I/\mathcal{G}^\infty_0$, where $\mathcal{G}^I$ consists of boundary-preserving gauge transformations asymptoting to a constant, and $\mathcal{G}^\infty_0$ consists of transformations generated by the Gauss law constraint. We rigorously derive this physical gauge group for both Abelian and non-Abelian theories. A key result is that restricting to $\mathcal{G}^I$ follows from the structure of the instantaneous state space on which the instantaneous Lagrangian is defined. We extend our analysis to Yang-Mills-Higgs theory, showing that boundary conditions and the physical gauge group differ between the unbroken and broken phases. |
| title | Global Gauge Symmetries and Spatial Asymptotic Boundary Conditions in Yang-Mills theory |
| topic | Mathematical Physics High Energy Physics - Theory History and Philosophy of Physics 70S15 (Primary) 70S05, 70S10, 53D20 (Secondary) |
| url | https://arxiv.org/abs/2502.16151 |