2D discrete Yang-Mills equations on the torus
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929452042158080 |
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| author | Sushch, Volodymyr |
| author_facet | Sushch, Volodymyr |
| contents | In this paper, we introduce a discretization scheme for the Yang-Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define discrete versions of the exterior covariant derivative operator and its adjoint, which capture essential geometric features similar to their continuous counterparts. Our focus is on discrete models defined on a combinatorial torus, where the discrete Yang-Mills equations are presented in the form of both a system of difference equations and a matrix form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 2D discrete Yang-Mills equations on the torus Sushch, Volodymyr Mathematical Physics Numerical Analysis 39A12, 39A70, 81T13 In this paper, we introduce a discretization scheme for the Yang-Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define discrete versions of the exterior covariant derivative operator and its adjoint, which capture essential geometric features similar to their continuous counterparts. Our focus is on discrete models defined on a combinatorial torus, where the discrete Yang-Mills equations are presented in the form of both a system of difference equations and a matrix form. |
| title | 2D discrete Yang-Mills equations on the torus |
| topic | Mathematical Physics Numerical Analysis 39A12, 39A70, 81T13 |
| url | https://arxiv.org/abs/2405.15315 |