The Reggeization of the Bethe-Salpeter Scattering Amplitudes

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概要

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• The Reggeization of the Bethe-Salpeter amplitude is investigated with general kernels. Assuming some integral representations for the interaction kernels and the modified propagator of the scattering particles with unequal masses, we obtain a sufficient condition for the kernels to be of the Hilbert-Schmidt type. Provided that this condition is satisfied, we prove the following, by studying the meromorphy domain of the partial-wave amplitudes: 1) the Sommerfeld-Watson transformation can be performed, 2) the asymptotic behavior of the leading trajectory as s→-∞ (s: total mass squared) is determined by the rightmost fixed singularity of the kernels, and 3) if the spectral functions of the integral representations are non-negative definite, the derivative of the largest eignvalue μ_<Max>(s,l)={λ_<Min>(s,l)}^<-1> with respect to the angular momentum l is negative for s<0 and l>-1, and the leading trajectory is real for s<0 and is nondegenerate.

• 理論物理学刊行会の論文
• 1970-11-25

著者

• Matsumoto Hideki

  Institute For Materials Research Tohoku University

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• The Reggeization of the Bethe-Salpeter Scattering Amplitudes

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