Eigenvalues of the Bethe-Salpeter Equation

概要

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In connection with the gauge dependence of the eigenvalues for a composite particle the weak binding limit of the Wick-Cutkosky model is examined closely. A simple and effective iteration procedure is devised to get an asymptotic expansion of the eigenvalue for the normal solutions. The formulas of first and second order are given explicitly. They show that the convergence is much slower than that of the usual potential model owing to spurious retardation effects. Nevertheless our procedure maintains relativistic covariance in contrast with the usual procedure. The difference between the nonrelativistic limit and the weak binding limit is shown explicitly in terms of the Bethe-Salpeter amplitude. For an arbitrary binding strength, approximate eigenvalue formulas are also given.
理論物理学刊行会の論文
1978-08-25