Solving the Bethe-Salpeter Equation in Minkowski Space: Scalar Theories and Beyond
Abstract
The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is solved in Euclidean space after a Wick rotation. For all but the lowest-order (i.e., ladder) approximation to the scattering kernel, the {\it naive} Wick rotation is invalid. Our approach generates the vertex function and Bethe-Salpeter amplitude for the entire allowed range of momenta, whereas these cannot be directly obtained from the Euclidean space solution. Our method is quite general and can be applied even in cases where the Wick rotation is not possible.
Keywords
Cite
@article{arxiv.hep-ph/9601364,
title = {Solving the Bethe-Salpeter Equation in Minkowski Space: Scalar Theories and Beyond},
author = {K. Kusaka and K. M. Simpson and A. G. Williams},
journal= {arXiv preprint arXiv:hep-ph/9601364},
year = {2015}
}
Comments
16 pages of LaTeX, uses epsfig.sty with 2 figures. Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html or ftp://adelphi.adelaide.edu.au/pub/theory/ADP-96-1.T206.ps