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arXiv · 2307.03149

Joint evolution of a Lorentz-covariant massless scalar field and its point-charge source in one space dimension

Lawrence Frolov·Samuel Leigh·A. Shadi Tahvildar-Zadeh
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Abstract

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.

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Lawrence Frolov, Samuel Leigh, A. Shadi Tahvildar-Zadeh. 2023-07-06. Joint evolution of a Lorentz-covariant massless scalar field and its point-charge source in one space dimension. https://arxiv.org/abs/2307.03149

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