O(3, 1) Harmonics and Its Application to Bethe-Salpeter Equation

概要

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The O(3, 1) harmonics are introduced as an extension of the O(2, 1) ones given by SertorioToller and are applied to solve the Bethe-Salpeter equation in the Wick-Cutkosky model without using the Wick-rotation. It is shown that the equation has physically unacceptable eigenvalues corresponding with complex-valued coupling constants which are connected to the eigenvalues known already through the O(4) symmetry by an analytical continuation in the four-dimensional angular momentum quantum number. On the other hand, it is shown that the solutions through the O(4) symmetry themselves cannot become solutions in our approach in a strict sense. The lightlike limit of the harmonics are also discussed, where the E(2) harmonics are derived as a limit of the O(3, 1) ones.
理論物理学刊行会の論文
1971-10-25