Renormalization in the New Tamm-Dancoff Theory of Meson-Nucleon Scattering

R. H. Dalitz and F. J. Dyson
Phys. Rev. 99, 301 – Published 1 July 1955
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Abstract

The new Tamm-Dancoff equations for meson-nucleon scattering are set up in the lowest approximation and it is shown how explicit nonphysical singularities may be avoided in these equations. The particle self-energies appearing in the integral equation are renormalized, but the resulting modified propagator for the system then has a nonphysical singularity. For the states T=j=12, the vertex and self-energy expressions generated by the uncrossed graph are considered. The renormalized vertex may be constructed by the successive solution of two one-dimensional integral equations, the finite part of the self-energy then being obtained by quadratures. Vertex renormalization is uncertain to a constant factor in the S12 state, and the S12 theory therefore depends on two parameters. No numerical results are obtained, owing to a number of difficulties found in this theory—a comparison is made between these difficulties and those of the corresponding Bethe-Salpeter equation.

  • Received 24 December 1954

DOI:https://doi.org/10.1103/PhysRev.99.301

©1955 American Physical Society

Authors & Affiliations

R. H. Dalitz*

  • Laboratory of Nuclear Studies, Cornell University, Ithaca, New York

F. J. Dyson

  • Institute for Advanced Studies, Princeton, New Jersey

  • *On leave of absence from the Department of Mathematical Physics, University of Birminghan, England.

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Vol. 99, Iss. 1 — July 1955

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