Relative velocity in special relativity and quantum field theory

TL;DR

This paper derives the relativistic relative velocity using Lorentz invariant quantities and reveals an arbitrariness in the standard cross-section definition.

Contribution

It provides a Lorentz invariant derivation of relative velocity and highlights ambiguities in the conventional cross-section formulation.

Findings

Relativistic relative velocity can be expressed via Lorentz invariant quantities.

There exists an arbitrariness in the standard definition of cross-section.

The derivation clarifies the foundational aspects of relativistic scattering theory.

Abstract

A derivation of the relative velocity used in the definition of the relativistic cross-section is given in terms of manifestly Lorentz invariant quantities. Along the way we find that there is a certain arbitrariness in the usual definition of cross-section.