A relativistic massive particle is described by a timelike worldline with proper-time four-velocity . In signature its normalization is and its momentum is . The relativistic charged-particle action adds electromagnetic coupling, whose variation gives the Lorentz force.
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A relativistic particle refers to a particle that is moving at speeds close to the speed of light, where the effects of Einstein's theory of relativity become significant. In the realm of classical physics, particles are described by Newtonian mechanics, which assumes that velocities are much less than the speed of light. However, when particles approach relativistic speeds (typically a significant fraction of the speed of light, denoted as \(c\)), their behavior can no longer be accurately described by classical mechanics.