Lorentz-equivariant flow with four delays of neutral type

TL;DR

This paper introduces a Lorentz-equivariant flow model with four delays of neutral type, extending electrodynamics to include a second interaction in the lightcone, and analyzes its properties including velocity discontinuities and special motion segments.

Contribution

It generalizes electrodynamics with a second lightcone interaction, defining a semiflow with complex delays and nonlinear gyroscopic terms, and explores boundary conditions for velocity discontinuities.

Findings

Defines a semiflow with four state-dependent delays of neutral type.

Analyzes propagation of velocity discontinuities and boundary layer neighborhoods.

Identifies special motion segments with constant velocities and vanishing accelerations.

Abstract

We generalize electrodynamics with a second interaction in lightcone. The time-reversible equations for two-body motion define a semiflow on $C^2(\mathbb{R})$ with four state-dependent delays of neutral type and nonlinear gyroscopic terms. Furthermore, if the initial segment includes velocity discontinuities, their propagation requires two energetic corner conditions defining boundary layer neighborhoods of large velocities and small denominators. Finally, we discuss a motion restricted to a straight line and a segment pair with vanishing accelerations that iterates to another constant-velocity segment pair.