% miko:type: atomic
% miko:title: Relativistic Energy-Momentum
% miko:summary: The invariant relation connecting energy, momentum, and rest mass.
% miko:tags: relativity
% miko:difficulty: undergrad
% miko:related: lorentz-transformation, four-vector, dirac-equation, klein-gordon-equation
% miko:keywords: energy, momentum, mass shell

\documentclass{article}
\usepackage{amsmath}
\title{Relativistic Energy-Momentum}
\begin{document}
\maketitle

\section{Relation}

The invariant relation is

$$
E^2=p^2c^2+m^2c^4.
$$

For a particle at rest, this reduces to $E=mc^2$.

\section{Four-Momentum}

The four-momentum is

$$
p^\mu=\left(\frac{E}{c},\mathbf p\right).
$$

Its invariant norm gives the mass shell condition.

\end{document}
