% miko:type: atomic
% miko:title: Dirac Equation
% miko:summary: A first-order relativistic equation for spin-one-half fields.
% miko:tags: particle
% miko:difficulty: undergrad
% miko:related: complete-particle-physics, klein-gordon-equation, standard-model
% miko:keywords: spinor, gamma matrices, antimatter

\documentclass{article}
\usepackage{amsmath}
\title{Dirac Equation}
\begin{document}
\maketitle

\section{Equation}

The free Dirac equation is

$$
(i\hbar c\gamma^\mu\partial_\mu-mc^2)\psi=0.
$$

The matrices $\gamma^\mu$ are chosen so that applying the operator twice
recovers the relativistic energy-momentum relation.

\section{Significance}

The equation naturally contains spin and predicts antiparticle degrees of
freedom. It is a prototype for fermion fields in the Standard Model.

\end{document}
