= Dirac equation
{c}
{title2=$(i\gamma^\mu\partial_\mu-m)\psi=0$}
{wiki}
The Dirac equation is the relativistic <equation of motion> for a <spin>-one-half <Dirac field>, $(i\gamma^\mu\partial_\mu-m)\psi=0$, in units $\hbar=c=1$. The <gamma matrices> obey the <Clifford algebra>, ensuring that each component also obeys the free <Klein-Gordon equation>.
Being first order in time allows an initial <spinor> to determine its subsequent free evolution. The components encode <spin> as well as <particle> and <antiparticle> solutions; quantization interprets both kinds of excitation with positive physical <energy>. Coupling through the <gauge covariant derivative> describes an <electron> interacting with an <electromagnetic field>. The nonrelativistic limit contains the coupling of <spin> to a <magnetic field>, explaining why a scalar relativistic wave equation alone cannot describe an <electron>.
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