where the scalar field is complex, F μ μ ν ν = ∂ ∂ μ μ A ν ν − − ∂ ∂ ν ν A μ μ is the electromagnetic field tensor, and D μ μ = ∂ ∂ μ μ − − i ( e / ℏ ℏ c ) A μ μ the covariant derivative containing the electric charge e of the electromagnetic field.