  Independent of assumptions about the form of the quark-antiquark scattering
kernel we derive the explicit relation between the pion Bethe-Salpeter
amplitude, Gamma_pi, and the quark propagator in the chiral limit; Gamma_pi
necessarily involves a non-negligible gamma_5 gamma.P term (P is the pion
four-momentum). We also obtain exact expressions for the pion decay constant,
f_pi, and mass, both of which depend on Gamma_pi; and demonstrate the
equivalence between f_pi and the pion Bethe-Salpeter normalisation constant in
the chiral limit. We stress the importance of preserving the axial-vector
Ward-Takahashi identity in any study of the pion itself, and in any study whose
goal is a unified understanding of the properties of the pion and other
hadronic bound states.
