Laplace Transforms and the Diagonalization of Bethe-Salpeter Equations for Absorptive Parts

H. D. I. Abarbanel; L. M. Saunders

doi:10.1103/PhysRevD.2.711

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Laplace Transforms and the Diagonalization of Bethe-Salpeter Equations for Absorptive Parts

H. D. I. Abarbanel^* and L. M. Saunders

Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540

^*A. P. Sloan Foundation Fellow.

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Phys. Rev. D 2, 711 – Published 15 August, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.711

Abstract

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 Euclidian 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.

References (15)

M. Jacob and G. C. Wick, Ann. Phys. (N. Y.) 7, 404 (1959)
P. Winternitz at the Dublin Summer School, 1969 (unpublished) Rutherford Laboratory Report No. RPP/T/3 (unpublished)
"Multiperipheral Dynamics" given by M. L. Goldberger at the 1969 Erice Summer School, Princeton University report (unpublished)
M. Bander and C. Itzykson, Rev. Mod. Phys. 38, 330 (1966) ibid.38, 346 (1966)
S. Nussinov and J. Rosner [J. Math. Phys. 7, 1670 (1966)]
M. Toller, [Nuovo Cimento 37, 631 (1965)]
Higher Transcendental Functions, edited by A. Erdélyi (McGraw-Hill, New York, 1953), Vol. I
[7], Vol. II
[3]
D. Amati et al., Nuovo Cimento 26, 896 (1962)
[3]
S. Pinsky and W. I. Weisberger (unpublished)
E. Bloom et al., Phys. Rev. Letters 23, 930 (1969) M. Breidenbach et al., ibid. 23, 935 (1969)
M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1964), p. 595
[14], p. 605

[c1] M. Jacob and G. C. Wick, Ann. Phys. (N. Y.) 7, 404 (1959)

[c2] P. Winternitz at the Dublin Summer School, 1969 (unpublished) Rutherford Laboratory Report No. RPP/T/3 (unpublished)

[c3] "Multiperipheral Dynamics" given by M. L. Goldberger at the 1969 Erice Summer School, Princeton University report (unpublished)

[c4] M. Bander and C. Itzykson, Rev. Mod. Phys. 38, 330 (1966) ibid.38, 346 (1966)

[c5] S. Nussinov and J. Rosner [J. Math. Phys. 7, 1670 (1966)]

[c6] M. Toller, [Nuovo Cimento 37, 631 (1965)]

[c7] Higher Transcendental Functions, edited by A. Erdélyi (McGraw-Hill, New York, 1953), Vol. I

[c8] [7], Vol. II

[c9] [3]

[c10] D. Amati et al., Nuovo Cimento 26, 896 (1962)

[c11] [3]

[c12] S. Pinsky and W. I. Weisberger (unpublished)

[c13] E. Bloom et al., Phys. Rev. Letters 23, 930 (1969) M. Breidenbach et al., ibid. 23, 935 (1969)

[c14] M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1964), p. 595

[c15] [14], p. 605

Physical Review D

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Laplace Transforms and the Diagonalization of Bethe-Salpeter Equations for Absorptive Parts

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