RELATIVISTIC FIELD-THEORETICAL FORMULATION OF THE THREE-DIMENSIONALEQUATIONS FOR THE THREE FERMION SYSTEM

Fizika B (Zagreb)

A. I. MACHAVARIANI¹ 

关键词: three-fermion systems;    relativistic equations;    Faddeev equations;    Lippmann-Schwinger-type equations;   

DOI  :  

学科分类：物理（综合）

来源: Fizika B: a journal of experimental and theoretical physics

【 摘 要 】

A new kind of the relativistic equations for the three-fermion systems are suggested.These equations are derived in the framework of the standard field-theoretical S-matrixapproach in the time-ordered three-dimensional form. Therefore the correspondingrelativistic covariant equations are three-dimensional from the beginning and theconsidered formulation is free of the ambiguities which appear due to a three-dimensionalreduction of the four-dimensional Bethe-Salpeter equations. The solutions of theconsidered equations satisfy automatically the unitarity condition, and for the leptons,these equations are exactly gauge invariant even after the truncation over themultiparticle (n > 3) intermediate states. Moreover, the form of these three-bodyequations does not depend on the choice of the model Lagrangian and it is the same for theformulations with and without quark degrees of freedom. The effective potential of thesuggested equations is defined by the vertex functions with two on-mass shell particles.It is emphasized that these INPUT vertex functions can be constructed from experimentaldata. Special attention is given to the comparison with the three-body Faddeev equations.Unlike these equations, the suggested three-body equations have the form of theLippmann-Schwinger-type equations with the connected potential. In addition, themicroscopical potential of the suggested equations contains the contributions from thethree-body forces and from the particle creation (annihilation) mechanism on the externalparticles. The structure of the three-body forces, appearing in the consideredfield-theoretical formulation, is analyzed.

【 授权许可】

Unknown