Solving Bethe-Salpeter equation in Minkowski space
V.A. Karmanov, J. Carbonell
TL;DR
This paper introduces a novel method for solving the Bethe-Salpeter equation directly in Minkowski space by combining light-front projection and Nakanishi representation, applicable to various kernels, and validated against known solutions.
Contribution
The authors develop a new Minkowski-space solution technique for the Bethe-Salpeter equation using light-front projection and Nakanishi representation, applicable to any kernel from Feynman graphs.
Findings
Reproduces Wick-Cutkosky equation analytically for massless exchange.
Numerical results match Wick rotation methods for massive exchange.
Method is valid for any kernel from irreducible Feynman graphs.
Abstract
We develop a new method of solving Bethe-Salpeter (BS) equation in Minkowski space. It is based on projecting the BS equation on the light-front (LF) plane and on the Nakanishi integral representation of the BS amplitude. This method is valid for any kernel given by the irreducible Feynman graphs. For massless ladder exchange, our approach reproduces analytically the Wick-Cutkosky equation. For massive ladder exchange, the numerical results coincide with the ones obtained by Wick rotation.
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