= Gamma matrices
{title2=$\gamma^\mu$}
{wiki}
= Gamma matrix
{synonym}
= Dirac gamma matrix
{c}
{synonym}
<Gamma matrices> represent the spacetime <Clifford algebra> through
$$
\gamma^\mu\gamma^\nu+\gamma^\nu\gamma^\mu=2\eta^{\mu\nu}I.
$$
For the <Minkowski metric> with signature $(+,-,-,-)$, $\gamma^0$ squares to $I$ and each spatial <gamma matrix> squares to $-I$. Distinct orthogonal generators anticommute. A four-dimensional <complex representation> is used for <Dirac spinors> in four-dimensional spacetime.
The particular <matrix> entries depend on the chosen <basis>; simultaneous <similarity transformations> preserve the defining relations. Their usefulness in the <Dirac equation> is that contracting them with derivatives produces a first-order operator whose square reduces to the second-order relativistic wave operator, apart from interactions or curvature contributions.
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