Relativistic bound-state equations in three dimensions
| dc.creator | Phillips, D. R. | |
| dc.creator | Wallace, S. J. | |
| dc.date | 1996-03-07 | |
| dc.date | 1996-05-16 | |
| dc.date.accessioned | 2026-07-07T11:15:41Z | |
| dc.date.available | 2026-07-07T11:15:41Z | |
| dc.description | Firstly, a systematic procedure is derived for obtaining three-dimensional bound-state equations from four-dimensional ones. Unlike ``quasi-potential approaches'' this procedure does not involve the use of delta-function constraints on the relative four-momentum. In the absence of negative-energy states, the kernels of the three-dimensional equations derived by this technique may be represented as sums of time-ordered perturbation theory diagrams. Consequently, such equations have two major advantages over quasi-potential equations: they may easily be written down in any Lorentz frame, and they include the meson-retardation effects present in the original four-dimensional equation. Secondly, a simple four-dimensional equation with the correct one-body limit is obtained by a reorganization of the generalized ladder Bethe-Salpeter kernel. Thirdly, our approach to deriving three-dimensional equations is applied to this four-dimensional equation, thus yielding a retarded interaction for use in the three-dimensional bound-state equation of Wallace and Mandelzweig. The resulting three-dimensional equation has the correct one-body limit and may be systematically improved upon. The quality of the three-dimensional equation, and our general technique for deriving such equations, is then tested by calculating bound-state properties in a scalar field theory using six different bound-state equations. It is found that equations obtained using the method espoused here approximate the wave functions obtained from their parent four-dimensional equations significantly better than the corresponding quasi-potential equations do. | |
| dc.description | 28 pages, RevTeX, 6 figures attached as postscript files. Accepted for publication in Phys. Rev. C. Minor changes from original version do not affect argument or conclusions | |
| dc.identifier | https://arxiv.org/abs/nucl-th/9603008 | |
| dc.identifier | http://arxiv.org/abs/nucl-th/9603008 | |
| dc.identifier | Phys.Rev.C54:507-522,1996 | |
| dc.identifier | doi:10.1103/PhysRevC.54.507 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/192464 | |
| dc.subject | Nuclear Theory | |
| dc.subject | High Energy Physics - Phenomenology | |
| dc.title | Relativistic bound-state equations in three dimensions | |
| dc.type | text |