A pair of chiral fermions ψ ψ + , ψ ψ ¯ ¯ + , one being the conjugate variable of the other, can be described in terms of a chiral boson ϕ ϕ ψ ψ + =: exp ⁡ ⁡ ( + i ∫ ∫ ∞ ∞ z ∂ ∂ + + ϕ ϕ ) : , ψ ψ ¯ ¯ + =: exp ⁡ ⁡ ( − − i ∫ ∫ ∞ ∞ z ∂ ∂ + + ϕ ϕ ) : where the currents of these two models are related by ∂ ∂ + + ϕ ϕ =: ψ ψ ¯ ¯ + ψ ψ + : where composite operators must be defined by a regularization and a subsequent renormalization.