Solving the Bethe-Salpeter Equation for Scalar Theories in Minkowski Space

Details Solving the Bethe-Salpeter Equation for Scalar Theories in Minkowski Space Solving the Bethe-Salpeter Equation for Scalar Theories in Minkowski Space

1995-01-11

arxiv.org/abs/hep-ph/9501262v1

Phys.Rev.D51:7026-7039,1995

Physics

High Energy Physics

High Energy Physics - Phenomenology

23 pages with 3 uuencoded, compressed Postscript figures. Entire manuscript available as a ps file at http://www.physics.ade

Scientific paper

10.1103/PhysRevD.51.7026

The Bethe-Salpeter (BS) equation for scalar-scalar bound states in scalar theories without derivative coupling is formulated and solved in Minkowski space. This is achieved using the perturbation theory integral representation (PTIR), which allows these amplitudes to be expressed as integrals over weight functions and known singularity structures and hence allows us to convert the BS equation into an integral equation involving weight functions. We obtain numerical solutions using this formalism for a number of scattering kernels to illustrate the generality of the approach. It applies even when the na\"{\i}ve Wick rotation is invalid. As a check we verify, for example, that this method applied to the special case of the massive ladder exchange kernel reproduces the same results as are obtained by Wick rotation.

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