4 research outputs found
O(4) Expansion of the ladder Bethe-Salpeter equation
The Bethe-Salpeter amplitude is expanded on a hyperspherical basis, thereby
reducing the original 4-dimensional integral equation into an infinite set of
coupled 1-dimensional ones. It is shown that this representation offers a
highly accurate method to determine numerically the bound state solutions. For
generic cases only a few hyperspherical waves are needed to achieve
convergence, both for the ground state as well as for radially or orbitally
excited states. The wave function is reconstructed for several cases and in
particular it is shown that it becomes independent of the relative time in the
nonrelativistic regime.Comment: 21 pages, revte
Nonperturbative study of generalized ladder graphs in a \phi^2\chi theory
The Feynman-Schwinger representation is used to construct scalar-scalar bound
states for the set of all ladder and crossed-ladder graphs in a \phi^2\chi
theory in (3+1) dimensions. The results are compared to those of the usual
Bethe-Salpeter equation in the ladder approximation and of several
quasi-potential equations. Particularly for large couplings, the ladder
predictions are seen to underestimate the binding energy significantly as
compared to the generalized ladder case, whereas the solutions of the
quasi-potential equations provide a better correspondence. Results for the
calculated bound state wave functions are also presented.Comment: 5 pages revtex, 3 Postscripts figures, uses epsf.sty, accepted for
publication in Physical Review Letter
Bound state solutions of scalar QED_{2+1} for zero photon mass
The Feynman-Schwinger representation is used to study the behavior of
solutions of scalar QED in (2+1) dimensions. The limit of zero photon mass is
seen to be smooth. The Bethe-Salpeter equation in the ladder approximation also
exhibits this property. They clearly deviate from the behavior in the
nonrelativistic limit. In a variational analysis we show that this difference
can be attributed to retardation effects of relativistic origin.Comment: LaTeX, 11 pages, 2 Postscript figures; uses `elsart.sty' and
`epsf.sty' (both included with the figures in one uuencoded-
compressed-tar-package); accepted for publication in Physics Letters B.
(elsart12.sty now also included