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The Dirac field transforms as the unconstrained spinor, and it satisfies the Dirac equation. The usual free Lagrangian for the Dirac field is
The Dirac fields are important components of Quantum electrodynamics and the Standard model.
A Dirac field is equivalent to two Majorana field s with the same mass.
A massless Dirac field is equivalent to two (massless) Weyl field s.