Current-Algebra Calculation of Hard-Pion Processes:A1→ρ+πandρ→π+π

New techniques are developed for treating the $n$-point functions of currents, which are interrelated by means of Ward identities obtained from the equal-time current commutation relations. The $n$-point functions are sorted out so as to define proper vertices which describe the reactions of particles of definite spin. A meson-dominance assumption is made by approximating the proper vertices by simple polynomials in momenta, with the coefficients determined by the Ward identities. The method is discussed in detail for $n=3\mathrm{}$ and the currents of chiral $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$, and then applied to the decay processes $A_1\to \rho +\pi$ and $\rho \to \pi +\pi$.