% miko:type: atomic
% miko:title: Four-Vector
% miko:summary: A spacetime vector transforming linearly under Lorentz transformations.
% miko:tags: relativity
% miko:difficulty: undergrad
% miko:related: lorentz-transformation, minkowski-interval, relativistic-energy-momentum
% miko:keywords: spacetime, Lorentz transformation, tensor

\documentclass{article}
\usepackage{amsmath}
\title{Four-Vector}
\begin{document}
\maketitle

\section{Definition}

A four-vector has components

$$
A^\mu=(A^0,A^1,A^2,A^3)
$$

that transform under Lorentz transformations.

\section{Invariant Product}

With metric $\eta_{\mu\nu}$,

$$
A\cdot B=\eta_{\mu\nu}A^\mu B^\nu
$$

is invariant.

\end{document}
