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Laplace transforms and the diagonalization of Bethe-Salpeter equations for absorptive parts. (English) Zbl 0197.26103
Summary: A Laplace transform is developed for the crossed-channel partial-wave analysis of Bethe-Salpeter-like equations for the absorptive part of scattering matrix elements. The transform requires no assumption about rotating contours to a Euclidean region and allows from the outset power growth in energy of the transformed absorptive part. This eliminates the need for any analytic continuation after the transformation. The diagonalization of the forward and nonforward equations with arbitrary irreducible kernels is explicitly carried out.

81Q40 Bethe-Salpeter and other integral equations arising in quantum theory
44A10 Laplace transform
quantum theory
Full Text: DOI
[1] M. Jacob, Ann. Phys. (N. Y.) 7 pp 404– (1959) · Zbl 0178.28304
[2] P. Winternitz, in: the Dublin Summer School, 1969
[3] M. Bander, Rev. Mod. Phys. 38 pp 330– (1966)
[4] M. Bander, Rev. Mod. Phys. 38 pp 346– (1966)
[5] S. Nussinov, J. Math. Phys. 7 pp 1670– (1966)
[6] M. Toller, Nuovo Cimento 37 pp 631– (1965)
[7] , in: Higher Transcendental Functions (1953) · Zbl 0051.30303
[8] D. Amati, Nuovo Cimento 26 pp 896– (1962)
[9] E. Bloom, Phys. Rev. Letters 23 pp 930– (1969)
[10] M. Breidenbach, Phys. Rev. Letters 23 pp 935– (1969)
[11] M. L. Goldberger, in: Collision Theory (1964)
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