COMPOSITE PARTICLES IN S-MATRIX THEORY AND IN FIELD THEORY

We give a model-independent exact solution in S-matrix terms to the problem of relating proper vertex functions and physical scattering amplitudes, a problem studied extensively by Ida. The solution is of the Omnès type, supplemented by the solution of some algebraic equations. We use conventional definitions of the renormalization constants Z1 and Z2 to study the composite limit (Z1=Z2=0) in S-matrix theory. A model-independent discussion of the same problem is given in terms of the Dyson equations, where essentially the same results are recovered, in a different language. Possible applications to the electromagnetic mass shifts of composite particles are briefly discussed, including problems of gauge invariance. © 1969 The American Physical Society.