Abstract. We use a Schrödinger wave equation formalism to solve the eikonal equation. We show that a solution to the eikonal equation is obtained in the limit as ~ → 0 of the solution to the corresponding linear Schrödinger equation. The Schrödinger equation corresponding to the eikonal turns out to be a generalized, screened Poisson equation. Despite being linear, it does not have a closed-for...

Generically coupled neutral scalar bosons and chiral fermions are shown, in the eikonal kinematical limit, to be described by a reduced (free field) theory with N = 1 on-shell supersymmetry. Charged scalars and spinors turn out to be described in the eikonal limit by a reduced interacting theory with a modified and restricted on-shell N = 1 supersymmetry. Consequences of such a symmetry for the...

We extend the algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei by combining the eikonal approximation for the scattering with a description of odd-mass nuclei in terms of the interacting boson-fermion model. We derive closed expressions for the transition matrix elements for one of the dynamical symmetries and discuss the interplay between collective and single...

We present a fast algorithm for solving the eikonal equation in three dimensions, based on the fast marching method. The algorithm is of the order O(N log N), where N is the total number of grid points in the computational domain. The algorithm can be used in any orthogonal coordinate system and globally constructs the solution to the eikonal equation for each point in the coordinate domain. Th...

The usual geometrical-optics expansion of the solution for the Helmholtz equation of a point source in an inhomogeneous medium yields two equations: an eikonal equation for the traveltime function, and a transport equation for the amplitude function. However, two difficulties arise immediately: one is how to initialize the amplitude at the point source as the wavefield is singular there; the ot...

The first-arrival quasi-P wave traveltime field in an anisotropic elastic solid solves a first-order nonlinear partial differential equation, the q P eikonal equation. The difficulty in solving this eikonal equation by a finitedifference method is that for anisotropic media the ray (group) velocity direction is not the same as the direction of the traveltime gradient, so that the traveltime gra...

Recently a concise expression for the subleading infrared singularity of dimensional-regularized gauge theories has been proposed. For conformal theories, such relation involves a universal eikonal contribution plus a non-eikonal contribution, related to the subleading term in the anomalous dimension of twist two operators with large spin. In this note we make use of the AdS/CF T correspondence...

In the framework of functional integration the non-leading terms to leading eikonal behavior of the Planckian-energy scattering amplitude are calculated by the straight-line path approximation. We show that the allowance for the first-order correction terms leads to the appearance of retardation effect. The singular character of the correction terms at short distances is also noted, and they ma...

We compare two non-perturbative techniques for calculating the singleparticle Green’s function of interacting Fermi systems with dominant forward scattering: our recently developed functional integral approach to bosonization in arbitrary dimensions, and the eikonal expansion. In both methods the Green’s function is first calculated for a fixed configuration of a background field, and then aver...

In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng and C.-W. Shu, A discontinuous Galerkin finite element method for directly solving ...