One-time equation for the scattering of a particle on a bound state in quantum field theory

Abstract

There is undoubted interest in the study of interaction processes in which systems of bound elementary particles participate. The quasipotential equation for the wav~ function of the bound states of several particles was constructed by Faustov [9]. The quasipotenttal approach made it possible to describe the basic properties of bound states in quantum electrodynamics avoiding many difficulties inherent in the fourdimensional Bethe- Salpeter formalism. The relativistic generalization of the three-dimensiona l Faddeev equations for the description of threeparticle systems was obtained by Kvinikhidze and Stoyanov [10] by a further development of the method proposed in [3]. In [11], Vinogradov derived relativistic Faddeev equations in the framework of the three-dimensional formulation of quantum field theory proposed by Kadyshevskii [12]. The results of these papers were obtained under the assumption that the quasipotential that describes interactions in a system of three particles can be represented as a sum of binary potentials. The present paper is devoted to the problem of describing the scattering of an elementary particle on a bound system of two other elementary particles in the framework of the one-time formulation of the relativistic many-body problem in quantum field theory. A quasipotential equation is obtained for the wave function that describes this scattering process. The effective interaction potential is expressed in terms of the binary interaction quasipotentials and also in terms of a quasipotential that cannot be reduced to a binary one.