SOLVING THE BETHE--SALPETER EQUATION IN MINKOWSKI SPACE: SCALAR THEORIES

Details SOLVING THE BETHE--SALPETER EQUATION IN MINKOWSKI SPACE: SCALAR THEORIES SOLVING THE BETHE--SALPETER EQUATION IN MINKOWSKI SPACE: SCALAR THEORIES

1995-05-02

arxiv.org/abs/hep-ph/9505208v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

8 pages, regular latex, no figures. Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home

Scientific paper

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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