Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2000-09-15
Phys.Rev. D63 (2001) 056002
Physics
High Energy Physics
High Energy Physics - Phenomenology
LaTeX, 23 pages, 2 figures, version to appear in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.63.056002
The Bethe-Salpeter formalism in the instantaneous approximation for the interaction kernel entering into the Bethe-Salpeter equation represents a reasonable framework for the description of bound states within relativistic quantum field theory. In contrast to its further simplifications (like, for instance, the so-called reduced Salpeter equation), it allows also the consideration of bound states composed of "light" constituents. Every eigenvalue equation with solutions in some linear space may be (approximately) solved by conversion into an equivalent matrix eigenvalue problem. We demonstrate that the matrices arising in these representations of the instantaneous Bethe-Salpeter equation may be found, at least for a wide class of interactions, in an entirely algebraic manner. The advantages of having the involved matrices explicitly, i.e., not "contaminated" by errors induced by numerical computations, at one's disposal are obvious: problems like, for instance, questions of the stability of eigenvalues may be analyzed more rigorously; furthermore, for small matrix sizes the eigenvalues may even be calculated analytically.
Lucha Wolfgang
Maung Khin Maung
Sch"oberl Franz F.
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