Proof of the Nambu-Goldstone realisation for vector-gluon-quark theories

A proof is given of the theorem that, in chiral-invariant vector-gluon theories, the spontaneous generation of fermion mass is associated with zero-mass pseudoscalar bosons. The proof relies heavily on the proper determination of Bethe-Salpeter kernels which respect the Ward identities correctly, and is exact to the extent that the propagator is self-consistently truncated. Given this result, we survey the implications of PCAC for the quark-gluon model.