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Composite Particles in S -Matrix Theory and in Field Theory
John M. Cornwall (University of Copenhagen, University of California, Los Angeles), Donald J. Levy (University of California, Los Angeles)
Abstract: 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 Omn\`es type, supplemented by the solution of some algebraic equations. We use conventional definitions of the renormalization constants ${Z}_{1}$ and ${Z}_{2}$ to study the composite limit (${Z}_{1}={Z}_{2}=0$) 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.