Terms involving ∂ ∂ μ μ ∂ ∂ μ μ U or ∂ ∂ μ μ ∂ ∂ μ μ U † † are not independent and can be brought to this form through partial integration. The constant F /4 is chosen in such a way that the Lagrangian matches the usual free term for massless scalar fields when written in terms of the pions,