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The Role of Boundary Conditions in Solving Finite-Energy, Two-Body, Bound-State Bethe-Salpeter Equations

G. B. Mainland
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Abstract

The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary conditions. The method discussed here for solving the Bethe-Salpeter equation requires only that the equation can be Wick rotated and that the two angular variables associated with rotations in three-dimensional space can be separated, properties that are possessed by many Bethe-Salpeter equations including all two-body, bound-state Bethe-Salpeter equations in the ladder approximation. The efficacy of the method is demonstrated by calculating finite-energy solutions to the partially-separated Bethe-Salpeter equation describing the Wick-Cutkosky model when the constituents do not have equal masses.

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G. B. Mainland. 2003-09-22. The Role of Boundary Conditions in Solving Finite-Energy, Two-Body, Bound-State Bethe-Salpeter Equations. https://doi.org/10.1016/j.jcp.2003.12.011

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