AN ITERATION OF THE SCATTERING MATRIX IN FINITE TERMS
WASHINGTON UNIV ST LOUIS MO
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Computation of collision cross section in quantum field theory are performed by evaluating the Tmatrix. The T-matrix is defined when the Hamiltonian can be separated into a free particle interaction. However the T-Matrix not being consistent with requirements for solution to free particle interaction is replaced by the R-Matrix. The R-Matrix was developed for the Hamiltonian on a free particle interaction. Results indicate that field theories can be classified into two varieties one kind which gives rise to finite weak coupling iterative expansions and another kind which gives rise to infinities. Presumably these latter infinites are indicative of some more deep seated pathology in the field equations or in the approximation by which a nonrelativistic Hamiltonian is obtained from a relativistic one. The gradient coupling theory, for example, gives rise to infinite R-Matrix elements, though these dont diverge as badly as the corresponding unrenormalized T-matrix elements evaluated by cut-off methods.