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The often used Gell-Mann-Oakes-Renner mass formula for Nambu-Goldstone (NG) bosons in QCD, such as the pions, involves the condensate $$, $f_{\pi}$ and the quark current masses. Within the context of the Global Colour Model (GCM) for QCD a manifestly different formula was recently found by Cahill and Gunner. Remarkably Langfeld and Kettner have shown the two formula to be equivalent. Here we note that the above recent analyses refer to the constituent pion and not the exact pion, even within the GCM. Further we generalise the Langfeld-Kettner identity to include the full response of the constituent quark propagators to the presence of a non-zero (and running) quark current mass., Comment: minor changes. 19 page Latex document

From QCD we derive a three-body Faddeev-type formulation of baryons, as qqq colour-singlet states bound by gluon exchange, which is covariant, has dynamically hidden chiral symmetry and incorporates the colour dynamics. The formulation exploits the dynamical role of colour "3 diquark substructure in baryons to simplify computations. For non-zero current quark masses the jP = ~ + and ~ - baryon octet mass formulae are shown to satisfy the Gell-Mann-Okubo and the Coleman-Glashow multiplet mass relationships.

We employ the functional integral formalism to study quantum chromodynamics (QCD) with Nf quarks of zero bare mass. In addition to local SU(Nc) colour symmetry, this theory possesses exact global G = UdNf)@UR(Nf) chiral symmetry. We obtain an exact bilocal Bose field representation of the generating functional which, as we prove after establishing the manner in which the bilocal fields transform under G, preserves the global chiral symmetry. We demonstrate how a local Bose field representation of the generating functional may be obtained from the bilocal bosonisation. This provides a direct link between QCD and low energy meson phenomenological models. We utilise the bilocal bosonisation in the study of the dynamical breakdown of the global chiral symmetry group G. We derive the vacuum field equation from the exact bilocal Bose field effective action and discuss two alternative solutions: one corresponding to a Wigner-Weyl realisation of the global symmetry group G in which the vacuum configuration is invariant under G; the other to a mixed realisation in which the vacuum manifold is the coset space G/H = U A(Nf ), where H = Uv(Nf ) is a subgroup of G.

Functional integral calculus (FIC) methods are used to transform the meson-diquark bosonisation of quantum chromodynamics into a meson-baryon effective action description of the low energy states of QCD-the adronisation of QCD.

We present a critical analysis of the Skyrmion model for baryons. Using model quantum field theories we determine the origin of meson chiral effective actions and show that Skyrmions, i.e. chiral topological solitons of these effective actions, cannot be related to baryons and that indeed Skyrmions in these models are unstable.