COVARIANT 3-BODY EQUATIONS IN PHI-3 FIELD-THEORY

We derive four-dimensional relativistic three-body equations for the c ase of a field theory with a three-Point interaction vertex. These equ ations describe the coupled 2 --> 2, 2 --> 3, and 3 --> 3 processes, a nd provide the means of calculating the kernel of the 2 --> 2 Bethe-Sa lpeter equation. Our equations differ from all previous formulations i n two essential ways. Firstly, we have overcome the overcounting probl ems inherent in earlier works. Secondly, we have retained all possible two-body forces when one particle is a spectator. In this respect, we show how it is necessary to also retain certain three-body forces as these can give rise to (previously overlooked) two-body forces when us ed in a 2 --> 3 process. The revealing of such hidden two-body forces gives rise to a further novel feature of our equations, namely, to the appearance of a number of subtraction terms. In the case of the piNN system, for example, the NN potential involves a subtraction term wher e two pions, exchanged between the nucleons, interact with each other through the pipi t-matrix. The necessity of an input pipi interaction is surprising and contrasts markedly with the corresponding three-dime nsional description of the piNN system where no such interaction expli citly appears. This illustrates the somewhat unexpected result that th e four-dimensional equations differ from the three-dimensional ones ev en at the operator level.