Abstract
We investigate the hypothesized existence of an S-matrix for gravity, and
some of its expected general properties. We first discuss basic questions
regarding existence of such a matrix, including those of infrared divergences
and description of asymptotic states. Distinct scattering behavior occurs in
the Born, eikonal, and strong gravity regimes, and we describe aspects of both
the partial wave and momentum space amplitudes, and their analytic properties,
from these regimes. Classically the strong gravity region would be dominated by
formation of black holes, and we assume its unitary quantum dynamics is
described by corresponding resonances. Masslessness limits some powerful
methods and results that apply to massive theories, though a continuation path
implying crossing symmetry plausibly still exists. Physical properties of
gravity suggest nonpolynomial amplitudes, although crossing and causality
constrain (with modest assumptions) this nonpolynomial behavior, particularly
requiring a polynomial bound in complex s at fixed physical momentum transfer.
We explore the hypothesis that such behavior corresponds to a nonlocality
intrinsic to gravity, but consistent with unitarity, analyticity, crossing, and
causality.
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