Non-Perturbative Four-Point Scattering from First-Quantized Relativistic JWKB release_jyy664gfdvdybmzxouyii25akq

Abstract

We apply the quantum mechanical (first-quantized) JWKB approximation to a two-body path integral describing the near-forward scattering of two relativistic, heavy, non-identical, scalar particles in D spacetime dimensions. In contrast to the loop expansion, in D = 4 this gives a strong-coupling expansion, and in D = 3 a non-perturbative weak-coupling expansion. When the interaction is mediated by massless quanta with spin N, we obtain explicit, relativistic results for the scattering amplitude when N = 0, 1 and 2. In D = 4 we find a Regge trajectory function that agrees with the usual quantum mechanical spectrum. We also find an exponentiated infrared divergence that becomes a pure phase factor when the Mandelstam invariants s and t are inside of the physical scattering region. In D = 3 we find a singularity whose position along the s axis is dependent on t. When the interaction is mediated by a heavy scalar with mass M, in D = 3 we find an all-order scattering amplitude where the multi-mass branch points t = (L + 1)^2M^2 appear as Regge poles.
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