Light-Front Bethe-Salpeter Equation
Abstract
A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests that the convergence of the expansion is rapid. This result is particular for light-front dynamics. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional ones. The technical procedure is developed for a two-boson case; the idea for an extension to fermions is given. The technical procedure appears quite practicable, possibly allowing one to go beyond the ladder approximation for the solution of the Bethe-Salpeter equation. The relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter equation and a corresponding quantum-mechanical description is discussed.
Cite
@article{arxiv.nucl-th/9909029,
title = {Light-Front Bethe-Salpeter Equation},
author = {J. H. O. Sales and T. Frederico and B. V. Carlson and P. U. Sauer},
journal= {arXiv preprint arXiv:nucl-th/9909029},
year = {2009}
}
Comments
42 pages, 5 figures