Non-abelian gauge theories of strong interactions and spectral-function sum rules

We present a diagram technique to isolate the leading singularities in the vacuum expectation values of current products, thereby making it possible to study the question of convergence of spectral-function sum rules associated with the currents. Working within asymptotically free theories, we derive certain sum rules, notable among them being Weinberg's first and second sum rules, which are shown to be valid if the strong interaction is globally SU(2) ×{} SU(2) invariant.