Non-Perturbative Four-Point Scattering from First-Quantized Relativistic
JWKB
release_jyy664gfdvdybmzxouyii25akq
by
M.E. Irizarry-Gelpí, W. Siegel
2016
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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