Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space

Details Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space

1997-05-13

arxiv.org/abs/hep-ph/9705298v2

Phys.Rev.D56:5071-5085,1997

Physics

High Energy Physics

High Energy Physics - Phenomenology

28 pages of LaTeX, uses psfig.sty with 5 figures. Also available via WWW at http://www.physics.adelaide.edu.au/theory/papers

Scientific paper

10.1103/PhysRevD.56.5071

We apply the perturbation theory integral representation (PTIR) to solve for the bound state Bethe-Salpeter (BS) vertex for an arbitrary scattering kernel, without the need for any Wick rotation. The results derived are applicable to any scalar field theory (without derivative coupling). It is shown that solving directly for the BS vertex, rather than the BS amplitude, has several major advantages, notably its relative simplicity and superior numerical accuracy. In order to illustrate the generality of the approach we obtain numerical solutions using this formalism for a number of scattering kernels, including cases where the Wick rotation is not possible.

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