## Abstract

It is argued that the relativistic Vlasov–Maxwell equations of the kinetic theory of plasma approximately describe a relativistic system of N charged point particles interacting with the electromagnetic Maxwell fields in a Bopp–Landé–Thomas–Podolsky (BLTP) vacuum, provided the microscopic dynamics lasts long enough. The purpose of this work is not to supply an entirely rigorous vindication, but to lay down a conceptual road map for the microscopic foundations of the kinetic theory of special-relativistic plasma, and to emphasize that a rigorous derivation seems feasible. Rather than working with a BBGKY-type hierarchy of n-point marginal probability measures, the approach proposed in this paper works with the distributional PDE of the actual empirical 1-point measure, which involves the actual empirical 2-point measure in a convolution term. The approximation of the empirical 1-point measure by a continuum density, and of the empirical 2-point measure by a (tensor) product of this continuum density with itself, yields a finite-N Vlasov-like set of kinetic equations which includes radiation-reaction and nontrivial finite-N corrections to the Vlasov–Maxwell–BLTP model. The finite-N corrections formally vanish in a mathematical scaling limit N? 8 in which charges ? 1 / vN. The radiation-reaction term vanishes in this limit, too. The subsequent formal limit sending Bopp’s parameter ?? 8 yields the Vlasov–Maxwell model.

Original language | English (US) |
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Pages (from-to) | 749-772 |

Number of pages | 24 |

Journal | Journal of Statistical Physics |

Volume | 180 |

Issue number | 1-6 |

DOIs | |

State | Published - Sep 1 2020 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

- Microscopic foundations
- Radiation-reaction corrections
- Relativistic plasma kinetic theory
- Vlasov-Maxwell system