Joint evolution of a Lorentz-covariant massless scalar field and its point-charge source in one space dimension
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929360489938944 |
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| author | Frolov, Lawrence Leigh, Samuel Tahvildar-Zadeh, A. Shadi |
| author_facet | Frolov, Lawrence Leigh, Samuel Tahvildar-Zadeh, A. Shadi |
| contents | In this paper we prove that the static solution of the Cauchy problem for a massless real scalar field that is sourced by a point charge in $1+1$ dimensions is asymptotically stable under perturbation by compactly-supported radiation. This behavior is due to the process of back-reaction. Taking the approach of Kiessling, we rigorously derive the expression for the force on the particle from the principle of total energy-momentum conservation. We provide a simple, closed form for the particle's self-action, and show that it is restorative in this model , i.e. proportional to negative velocity, and causes the charge to return to rest after the radiation passes through. We establish these results by studying the joint evolution problem for the particle-scalar field system, and proving its global well-posedness and the claimed asymptotic behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03149 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Joint evolution of a Lorentz-covariant massless scalar field and its point-charge source in one space dimension Frolov, Lawrence Leigh, Samuel Tahvildar-Zadeh, A. Shadi Analysis of PDEs Mathematical Physics 78A35, 35A21, 70S10 In this paper we prove that the static solution of the Cauchy problem for a massless real scalar field that is sourced by a point charge in $1+1$ dimensions is asymptotically stable under perturbation by compactly-supported radiation. This behavior is due to the process of back-reaction. Taking the approach of Kiessling, we rigorously derive the expression for the force on the particle from the principle of total energy-momentum conservation. We provide a simple, closed form for the particle's self-action, and show that it is restorative in this model , i.e. proportional to negative velocity, and causes the charge to return to rest after the radiation passes through. We establish these results by studying the joint evolution problem for the particle-scalar field system, and proving its global well-posedness and the claimed asymptotic behavior. |
| title | Joint evolution of a Lorentz-covariant massless scalar field and its point-charge source in one space dimension |
| topic | Analysis of PDEs Mathematical Physics 78A35, 35A21, 70S10 |
| url | https://arxiv.org/abs/2307.03149 |