As explained above, the axial current is simply the equivalent of the electromagnetic current for the axial symmetry instead of the U(1) symmetry. Another perspective is given by recalling that the chiral symmetry is the invariance of the theory under the field rotation ψ ψ L → → e i θ θ L ψ ψ L and ψ ψ R → → ψ ψ R (or alternatively ψ ψ L → → ψ ψ L and ψ ψ R → → e i θ θ R ψ ψ R ), where ψ ψ L denotes a left-handed field and ψ ψ R a right-handed one. From this as well as the fact that ψ ψ = ψ ψ L + ψ ψ R and the definition of j 5 μ μ above, one sees that the axial current is the difference between the current due to left-handed fermions and that from right-handed ones, whilst the electromagnetic current is the sum.