Particle Physics · undergrad

Dirac Equation

A first-order relativistic equation for spin-one-half fields.

Published Apr 26, 2026 · 1 min

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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.

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

A standard introductory path through relativistic waves, symmetries, the Standard Model, and neutrino mixing.

The relativistic wave equation associated with the energy-momentum relation for spin-zero fields.

The gauge theory describing known elementary particles and three fundamental interactions.