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The Tamm-Dancoff equations are expressed in a concise four-dimensional form. The difficulty of renormalizing the new Tamm-Dancoff equation of Dyson is discussed. The L\'evy-Klein approximation to the Bethe-Salpeter equation is derived as an approximation to the old Tamm-Dancoff equation, and a new renormalizable equation is derived analogously as an approximation to the new Tamm-Dancoff equation. The latter approximation is better than the former.
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J. C. Taylor (1954) studied this question.
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