Solving the Bethe-Salpeter Equation in Minkowski Space: Scalar Theories and Beyond

Details Solving the Bethe-Salpeter Equation in Minkowski Space: Scalar Theories and Beyond Solving the Bethe-Salpeter Equation in Minkowski Space: Scalar Theories and Beyond

1996-01-30

arxiv.org/abs/hep-ph/9601364v1

Austral.J.Phys.50:147-154,1997

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages of LaTeX, uses epsfig.sty with 2 figures. Entire manuscript available as a ps file at http://www.physics.adelaide.edu

Scientific paper

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.

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