Nonlinear equations for fields radiated by particles
type: Item
instance of: scholarly article
title: Nonlinear equations for fields radiated by particles
zbMATH Open document ID: 0545.35059
DOI: 10.1007/BF00400317
author: A. K. Pogrebkov
published in: Letters in Mathematical Physics
publication date: 1982-01-01T00:00:00Z
review text: This paper is devoted to the determination of the Poincaré invariant second order partial differential equations satisfied by the field radiated by a classical relativistic particle, described by its world line in n dimensional Minkowski space time \(M_ n\). The field is assumed to be retarded, namely, for each \(x\in M_ n\), to depend only on the unique point of the world line which is time like separated from x and in the past of x, and on a finite number of derivatives of the position of the particle with respect to its proper time, taken at that point. The equation is assumed in addition to be independent of the world line outside of the latter. The problem is solved completely for scalar fields, yielding (up to a change of function) the Liouville equation for \(n=2\), and the conformal invariant equation for scalar fields for \(n\geq 3\) (in particular the wave equation for \(n=4)\). In addition, the equation has a source term for \(n=4\). The problem is also solved for vector fields in some special cases (for instance under the Lorentz condition). The paper ends with some comments on the possibility of describing the Poincaré covariant evolution of a set of relativistic particles by considering them as the set of singularities of a field satisfying an invariant equation.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L10
Mathematics Subject Classification ID: 83A05
zbMATH DE Number: 3867840
zbMATH Keywords: radiation field
zbMATH Keywords: Poincaré invariant second order partial differential equations
zbMATH Keywords: Minkowski space time
zbMATH Keywords: Liouville equation
zbMATH Keywords: Lorentz condition
zbMATH Keywords: Poincaré covariant evolution
zbMATH Keywords: relativistic particles
reviewed by: Jean Ginibre
MaRDI profile type: Publication
cites work: Classical Electrodynamics in Terms of Direct Interparticle Action
cites work: Singular solitons: An example of a sinh-Gordon equation
description: scientific article; zbMATH DE number 3867840