Minimal coupling is the procedure by which the Dirac equation, which describes free relativistic spin-1/2 massive particles, is modified to include electromagnetic interaction by replacing the ordinary spacetime derivative with a gauge-covariant derivative incorporating the electromagnetic four-potential. This substitution is required to preserve gauge invariance — the principle that physical observables (electric and magnetic fields) remain unchanged under a gauge transformation of the potentials — and thereby keeps the equation consistent with both Lorentz covariance and electromagnetic gauge symmetry. The concept sits within relativistic quantum mechanics and quantum field theory, connecting the Dirac equation's description of fermions to gauge theory, with the massless limit reducing to the Weyl equation for chiral particles.
Minimal coupling is the procedure by which the Dirac equation, which describes free relativistic spin-1/2 massive particles, is modified to include electromagnetic interaction by replacing the ordina…