Absorptive parts and the Bethe-Salpeter equation for forward scattering

S. Nussinov*, J. Rosner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We have developed a Laplace transform approach to the Bethe-Salpeter equation for absorptive parts of forward scattering amplitudes. The method appears direct and unsophisticated and is useful for computation. It is essentially identical to decomposition into four-dimensional partial waves, but the inversion formula is more straightforward. We have obtained the high-energy behavior of sums of several types of Φ4 graphs in the weak- and strong-coupling limits. These examples illustrate some general results we obtain for Mth order Φ4 kernels. Specifically, the absorptive part behaves as sno(log s)β for high s; for weak coupling λ, n0 λiM, while for strong coupling in the ladder graph approximation, n0/λ1 → 1/2π. We have also proven an interesting inequality related to absorptive parts. One of its corollaries is that uncrossed ladder graphs "majorize" crossed ones.

Original languageEnglish
Pages (from-to)1670-1679
Number of pages10
JournalJournal of Mathematical Physics
Volume7
Issue number9
DOIs
StatePublished - 1966
Externally publishedYes

Fingerprint

Dive into the research topics of 'Absorptive parts and the Bethe-Salpeter equation for forward scattering'. Together they form a unique fingerprint.

Cite this