“Isochronic” dynamical systems and nullification of amplitudes

Abstract

We construct the set of theories which share the property that the tree-level threshold amplitudes nullify even if both initial and final states contain the same type of particles. The origin of this phenomenom lies in the fact that the reduced classical dynamics describes isochronic systems.

Multiboson threshold production by fermion–antifermion pair and hidden symmetry

“…Applying LSZ we get the generating function for matrix elements for purely soft processes f f → nρ. In analogy with scalar case we expect (14) to exhibit some hidden symmetry. Indeed, it is straightforward although tedious to check that it posses the integral of motion of the form…”

“…[11] were subsequently supported by diagrammatic [12] and functional [13] proofs of the relevant Ward identities expressing the underlying symmetry at the tree level. Moreover, they allowed to construct other models with vanishing soft-soft amplitudes [14]. One can pose the question whether the nullification of hard-soft amplitudes can be also explained as a consequence of some symmetry.…”

“…To find the relevant purely soft amplitudes we solve the equation of motion following from the lagrangian (14) together with the boundary condition (5) and…”