= Dirac field
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{wiki}
A Dirac field is a <quantum field> transforming as a <Dirac spinor>. Its free <Lagrangian density> is $\mathcal L=i\bar\psi\gamma^\mu\partial_\mu\psi-m\bar\psi\psi$, giving the <Dirac equation>. Unlike a single-particle <wave function>, a quantized Dirac field can create and remove <particles> and <antiparticles>.
Its <mode expansion of a Dirac field> contains <fermionic annihilation operators> for <particles> and <fermionic creation operators> for <antiparticles>, with <canonical anticommutation relations> enforcing <Fermi-Dirac statistics>. For the <electron> field, these excitations are <electrons> and <Positrons>. A global phase <symmetry> gives the conserved <Dirac current>; coupling that current to the <electromagnetic field> produces the matter interaction in <quantum electrodynamics>.
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