V. A. Matveev

Straight-line path method and the eikonal problem

ConclusionsThus, the study of the class of ladder diagrams in the scalar model shows that the eikonal formula corresponds to our allowing in the asymptotic behavior for then

Relativistic form factors of composite particles

overline t

Eikonal approximation in quantum field theory

n-paths that coincide with nucleon lines. In this case, the leading particle, which carries the large momentum, is a nucleon and it does not change its species in the virtual process. The noneikonal contributions to the scattering amplitude are due to processes in which the species of the leading particle changes, i.e., to a transfer of momentum from nucleons to mesons and vice versa. There then arises the important question of the role of “twisted” graphs corresponding to the original ladder graph with replacement of the final momenta q1↔q2 (compare Fig. 1 and formula (1.2)). The possibility of transferring a large momentum to a meson means that the contribution to the asymptotic behavior of the scattering amplitude may dominate over the eikonal contribution in the same order in the coupling constant. For example, in the fourth order, the “twisted” graph (see Fig. 16) has the asymptotic behavior 1n s/s.Note that whereas the orthodox eikonal formula corresponds to scattering on a Yukawa quasipotential due to one-meson exchange, allowance for the graph in Fig. 16 leads to the appearance of a correction to the quasipotential of non-Yukawa type. The correction we have found corresponds to the exchange of a nucleon-antinucleon pair and has effective range ∼h/2m, and behaves at short distances like 1n r/r.The example pointed out here demonstrates the importance of the study of the successive corrections to the effective quasipotential at high energies and speaks in favour of the quasipotential in quantum field theory.

Straight-line particle path approximation for high-energy hadron scattering in quantum field theory

Alongside the study of the general proper t ies of solutions of quasipotential equations, for example, in the f ramework of the assumption that the local quasipotentiat is smooth [9-12], interest attaches to developing different approximate methods. In the present paper, we propose an operator method of finding approximate solutions of quasipotential equations; the formulation of this method is given in the f i rs t section. We should point out that this method is fair ly general in nature and may be applied to other equations of quantum field theory.