Non-Abelian quantum field theory of pionic strong interactions

A renormalizable non-Abelian theory of strong interactions of pions, mediated by rho-mesons, is formulated at tree- and at one-loop level in perturbation theory. Hadron masses are generated through spontaneous symmetry breaking using the Higgs mechanism. Quantization and gauge fixing is achieved using the generalized class of $R_{\xi }$ gauges. As an application of this theory, pion-pion scattering lengths are obtained at tree-level in good agreement with data.