Results 1 - 10 of 20928
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[en] For Compton scattering amplitudes we derive the constraints and correlations of fairly general type at energies below photoproduction threshold and fixed momentum transfer, following from (an upper bound on) the corresponding differential cross section above photoproduction threshold. The derivation involves the solution of an extremal problem in a certain space of vector-valued analytic functions. (author)
[en] We present a formalism for computing classically measurable quantities directly from on-shell quantum scattering amplitudes. We discuss the ingredients needed for obtaining the classical result, and show how to set up the calculation to derive the result efficiently. We do this without specializing to a specific theory. We study in detail two examples in electrodynamics: the momentum transfer in spinless scattering to next-to-leading order, and the momentum radiated to leading order.
[en] We develop a manifestly supersymmetric version of the generalized unitarity cut method for calculating scattering amplitudes in N=4 SYM theory. We illustrate the power of this method by computing the one-loop n-point NMHV super-amplitudes. The result confirms two conjectures which we made in Drummond, et al., . Firstly, we derive the compact, manifestly dual superconformally covariant form of the NMHV tree amplitudes for arbitrary number and types of external particles. Secondly, we show that the ratio of the one-loop NMHV to the MHV amplitude is dual conformal invariant
[en] We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized “winding number”. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of “sign flips” of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural “dual” of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the configuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar SYM as a differential form on the space of physical kinematical data.
[en] Let V element-of Lc∞ (Rn) be a real-valued potential, n ≥ 3 odd. The scattering matrix, Sv(A), corresponding to V extends to be a meromorphic function in C. Our normalization is that P, the physical half plane, is the open lower half plane, C-. Thus, Sv(λ) only has a finite number of poles in P and they correspond to the bound states of the Hamiltonian Δ + V (Δ is the positive Laplacian). In Zworski has shown that the number of scattering poles n(r) in a disc of radius r is bounded by C(r + 1)n, and in he has given similar lower bounds for n(r) for certain radial potentials. The question of the existence of pure imaginary scattering poles was investigated by Lax and Phillips for both obstacle and potential scattering. In the case of obstacle scattering they showed that the number N(s) of pure imaginary scattering poles of absolute value less than s satisfies C1 s2< N(s) for n = 3 for some constant C1 > 0, and there is an analogous upper bound if the obstacle is star-shaped. They also proved that much of the machinery can be translated into the setting of potential scattering by non-negative potentials. This reduces the problem of obtaining lower bounds for N(s) to finding the corresponding bounds when V is tile characteristic function of a ball. In this paper we make the simple observation that their proof can be modified to accommodate non-positive potentials, and we prove that if V or -V is bounded below by a positive multiple of the characteristic function of a ball, then for some C, C' > 0
[en] We study wave scattering from a gently curved surface. We show that the recursive relations, implied by shift invariance, among the coefficients of the perturbative series for the scattering amplitude allow to perform an infinite resummation of the perturbative series to all orders in the amplitude of the corrugation. The resummed series provides a derivative expansion of the scattering amplitude in powers of derivatives of the height profile, which is expected to become exact in the limit of quasi-specular scattering. We discuss the relation of our results with the so-called small-slope approximation introduced some time ago by Voronovich.
[en] Scattering by the Helmholtz resonator is considered and the behaviour of the scattering amplitude near a resonance is studied. A relation between the symmetry properties of the resonator and the symmetry properties of the scattering amplitude is established