Nonperturbative effects in low energy effective theories of QCD

Abstract

In this talk I concentrate on the role of chiral symmetry realisation by spin-1 fields in the low energy QCD effective lagrangian. I assume that chiral symmetry is nonlinearly realised and that spin-1 fields transform homogeneously under chiral rotations, which is in sharp contrast to previous works where the $\rho$ and the $a_1$ mesons were treated as approximate gauge bosons of some chiral group. I emphasise the role played by four-meson couplings which in our scheme are essential for the theory to make sense. By requiring the kinetic energy density of the theory to be bounded from below we find inequalities relating three- and four-point meson couplings. It is finally shown how the combination of our analysis and of unitarity requirements naturally leads to a low-energy phenomenological lagrangian for the nonanomalous sector of $\pi\rho a_1$ strong interactions.