Sequences of co-moving Lorentz frames
The paper presents a new analysis of co-moving sequences of Lorentz reference frames tracking accelerated relativistic particles. The group property of the homogeneous Lorentz transformation written in the most general, coordinate-independent form for inertial frames with arbitrary orientation and velocity implies the composition law that is used to formulate the conditions of any co-moving sequence. These lead to a new differential equation of change which defines entire sequences and selects the frames within a given sequence, \(d\bar R/dt=- \bar Rx\omega_ T-\omega'x\bar R/\gamma\), where \(\bar R\) is an arbitrary rotation dydic, \(\gamma\) a parameter. It is governed by two arbitrary angular velocities, the velocity of Thomas precession \(\omega_ T\) and an arbitrary angular velocity \(\omega'\) between adjacent instantaneous frames. A formal integration of selection equation, which is generally unsoluble in closed form, is outlined using time-ordered operator products. This represents a perturbation solution. Coupled differential equations for the effective axis and angle of the rotation component of the Lorentz transformation are derived. Two specific examples are considered.
scientific article; zbMATH DE number 4175392