Partial wave amplitudes and multiparticle production

Recursion relations for integrals of amplitudes over the phase space, i.e. for partial wave amplitudes, are introduced. In their simplest form these integrals are proportional to the s-wave amplitudes and represent rigorous lower bounds on the total cross sections. The connection with classical field equations in $D$ dimensions is established. Previous results on multiparticle amplitudes are easily reproduced.