Partial diagonalization of absorptive part equations by laplace transforms

A Laplace transform is developed to perform a crossed channel partial wave analysis of Bethe-Salpeter equations for absorptive parts of nonforward scattering matrix elements involving particles with spin. The method requires no rotation of contours and allows from the outset power growth in energy o...

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Bibliographic Details
Published inAnnals of physics Vol. 64; no. 1; pp. 254 - 270
Main Authors Abarbanel, H.D.I, Saunders, L.M
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.1971
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Summary:A Laplace transform is developed to perform a crossed channel partial wave analysis of Bethe-Salpeter equations for absorptive parts of nonforward scattering matrix elements involving particles with spin. The method requires no rotation of contours and allows from the outset power growth in energy of the absorptive part. Diagonalization of the equation with an arbitrary kernel is explicitly carried out, thereby reducing it from a four-dimensional equation to a two-dimensional one. The analysis makes continual use of the underlying SO(1, 2) group symmetry in choosing kinematic variables, defining the transform and proving the crucial addition theorem necessary to effect the diagonalization.
ISSN:0003-4916
1096-035X
DOI:10.1016/0003-4916(71)90285-5