Dynamics of a relativistic discrete body: rigidity conditions, and covariant equations of motion

TL;DR

This paper proposes new rigidity conditions and covariant equations of motion for a relativistic discrete body, offering a more general framework than Born's theory with potential advantages.

Contribution

It introduces a novel set of rigidity conditions and compatible covariant equations of motion for relativistic bodies modeled as discrete particle systems.

Findings

The theory has six dynamical degrees of freedom.

It allows for more general motions than Born's rigidity-based approach.

Rigidity conditions alone do not determine the system's evolution.

Abstract

Rigidity conditions for a body considered as a discrete system of relativistic particles are proposed. They by themselves do not yet determine an evolution of the system, and some second-order equations must be added to them. Poincar\'e-covariant equations of motion compatible with these rigidity conditions are proposed and discussed. The resulting theory has the expected six dynamical degrees of freedom and therefore allows for more general motions than in Born's theory. Therefore, treating a relativistic body as a discrete system of particles could be a promising alternative to the standard approach based on Born's rigidity conditions.