Retrieving Yang--Mills--Higgs fields in Minkowski space from active local measurements
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929479763361792 |
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| author | Chen, Xi Lassas, Matti Oksanen, Lauri Paternain, Gabriel P. |
| author_facet | Chen, Xi Lassas, Matti Oksanen, Lauri Paternain, Gabriel P. |
| contents | We show that we can retrieve a Yang--Mills potential and a Higgs field (up to gauge) from source-to-solution type data associated with the classical Yang--Mills--Higgs equations in Minkowski space $\mathbb{R}^{1+3}$. We impose natural non-degeneracy conditions on the representation for the Higgs field and on the Lie algebra of the structure group which are satisfied for the case of the Standard Model. Our approach exploits the non-linear interaction of waves generated by sources with values in the centre of the Lie algebra showing that abelian components can be used effectively to recover the Higgs field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12776 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Retrieving Yang--Mills--Higgs fields in Minkowski space from active local measurements Chen, Xi Lassas, Matti Oksanen, Lauri Paternain, Gabriel P. Analysis of PDEs Mathematical Physics Differential Geometry We show that we can retrieve a Yang--Mills potential and a Higgs field (up to gauge) from source-to-solution type data associated with the classical Yang--Mills--Higgs equations in Minkowski space $\mathbb{R}^{1+3}$. We impose natural non-degeneracy conditions on the representation for the Higgs field and on the Lie algebra of the structure group which are satisfied for the case of the Standard Model. Our approach exploits the non-linear interaction of waves generated by sources with values in the centre of the Lie algebra showing that abelian components can be used effectively to recover the Higgs field. |
| title | Retrieving Yang--Mills--Higgs fields in Minkowski space from active local measurements |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2204.12776 |