Covariant light front perturbation theory and three-particle equations.

Abstract

A covariant version of light front perturbation theory is obtained as a limit of the covariant time-ordered perturbation theory developed recently by the author. The graphical rules for the covariant light front perturbation theory are essentially the same as Weinberg's infinite momentum frame rules; however, they involve a redefinition of the original Weinberg variables. The new definitions guarantee that the contributions of individual diagrams to the S matrix are invariant. A set of manifestly invariant three-particle integral equations is derived. These equations are obtained from a model field theory which describes the interaction of a charged scalar particle \ensuremath{\psi} with a neutral scalar particle \ensuremath{\varphi} according to the virtual process \ensuremath{\psi}\ensuremath{\rightleftarrows}\ensuremath{\psi}+\ensuremath{\varphi}. The solutions of the integral equations lead to amplitudes for \ensuremath{\varphi}+\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\varphi}+\ensuremath{\psi} and \ensuremath{\varphi}+\ensuremath{\psi}\ensuremath{\rightarrow}2\ensuremath{\varphi}+\ensuremath{\psi} which satisfy two- and three-particle unitarity. The integral equations are free of the spurious singularity in s, the square of the invariant c.m. energy, which has been an undesirable feature of earlier relativistic three-particle equations. This singularity is known to be responsible for spurious bound state solutions.