The charge conjugation involution is then the mapping formula_110 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: formula_111 and formula_112 and so, for the complexified field, charge conjugation is just formula_113 The "mapsto" arrow formula_114 is convenient for tracking "what goes where"; the equivalent older notation is simply to write formula_115 and formula_116 and formula_117