where γ are Dirac matrices, ψ ψ ¯ ¯ = ψ ψ † † γ γ 0 , and F μ μ ν ν = ∂ ∂ μ μ A ν ν − − ∂ ∂ ν ν A μ μ is the electromagnetic field strength. The parameters in this theory are the (bare) electron mass m and the (bare) elementary charge e. The first and second terms in the Lagrangian density correspond to the free Dirac field and free vector fields, respectively. The last term describes the interaction between the electron and photon fields, which is treated as a perturbation from the free theories.