Multivariable Expansion of the Scattering Amplitude Involving an Arbitrary Number of Spinless Particles; Crossing Symmetry for Partial Waves
We derive an infinite number of sum rules for the scattering processes involving any finite number of spinless particles. Each sum rule involves a finite number of partial-wave amplitudes from direct and crossed channels. These sum rules are implied by the crossing symmetry of the system and are complete. We classify these sum rules into an independent set, thus obtaining a basis for multivariable expansion. This basis displays the threshold and pseudothreshold zeros and kinematic singularities of the partial waves.