The relativistic mechanics in a nonholonomic setting: A unified approach to particles with non-zero mass and massless particles

TL;DR

This paper introduces a unified geometric framework for relativistic particle dynamics, accommodating particles with any mass, including massless and tachyonic, revealing new forces from nonholonomic constraints.

Contribution

It develops a novel nonholonomic geometric approach to relativistic mechanics that unifies descriptions of particles with different mass types and derives new force terms.

Findings

Derived equations of motion for all mass types.

Identified new forces from nonholonomic constraints.

Analyzed dynamics of tachyons and massless particles.

Abstract

A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred manifolds. A setting based on a natural Lagrangian and a constraint on four-velocity of a particle is proposed, that allows a unified approach to particles with any (positive/negative/zero) square of mass. The corresponding equations of motion are obtained and discussed. In particular, new forces are found (different from the usual Lorentz force type term), arising due to the nonholonomic constraint. A possible meaning and relation with forces previously proposed by Dicke is discussed. In particular, equations of motion of tachyons and of massless particles are studied and the corresponding dynamics are investigated.