The charge conjugation involution is then the mapping C : i ↦ ↦ − − i since this is sufficient to reverse the sign on the electromagnetic potential (since this complex number is being used to couple to it). For real scalar fields, charge conjugation is just the identity map: C : ϕ ϕ ↦ ↦ ϕ ϕ and C : χ χ ↦ ↦ χ χ and so, for the complexified field, charge conjugation is just C : ψ ψ ↦ ↦ ψ ψ ∗ ∗ . The "mapsto" arrow ↦ ↦ is convenient for tracking "what goes where"; the equivalent older notation is simply to write C ϕ ϕ = ϕ ϕ and C χ χ = χ χ and C ψ ψ = ψ ψ ∗ ∗ .