The theory establishes that charged fermion fields described by the Dirac equation interact with external electromagnetic potentials through a minimal coupling substitution ($p_\mu \to p_\mu - qA_\mu$), which introduces interaction terms in the Hamiltonian proportional to $e\gamma^0 A^\mu$. Formally, this leads to the identification of a conserved four-vector current density $j^\mu = e\bar{\psi}\gamma^\mu\psi$, where $\bar{\psi}$ denotes the Dirac adjoint. In Quantum Electrodynamics (QED), the transition amplitude for scattering processes is expressed as an integral over space-time involving this vector current coupled to the electromagnetic four-potential, mathematically yielding a photon propagator term proportional to $g_{\mu\nu}/q^2$. This mechanism defines the fundamental rule of how elementary charged particles exchange virtual photons via their respective currents within relativistic quantum field theory.
The theory establishes that charged fermion fields described by the Dirac equation interact with external electromagnetic potentials through a minimal coupling substitution ($p_\mu \to p_\mu - qA_\mu…