Constraints on Four-Point Couplings in Low-Energy Meson Interactions

We investigate from first principles the introduction of isospin-1 vector and axial-vector fields into the nonlinear sigma model. Chiral symmetry is nonlinearly realised and spin-1 fields are assumed to transform homogeneously under chiral rotations. By requiring the Hamiltonian of the theory to be bounded from below we find inequalities relating three- and four-point meson couplings. This leads to a low-energy phenomenological Lagrangian for the nonanomalous sector of $\pi\rho a_1$ strong interactions.