The evaluation of the 4-point Green functions in the 1+1 Schwinger model is
presented both in momentum and coordinate space representations. The crucial
role in our calculations play two Ward identities: i) the standard one, and ii)
the chiral one. We demonstrate how the infinite set of Dyson-Schwinger
equations is simplified, and is so reduced, that a given n-point Green function
is expressed only through itself and lower ones. For the 4-point Green
function, with two bosonic and two fermionic external `legs', a compact
solution is given both in momentum and coordinate space representations. For
the 4-fermion Green function a selfconsistent equation is written down in the
momentum representation and a concrete solution is given in the coordinate
space. This exact solution is further analyzed and we show that it contains a
pole corresponding to the Schwinger boson. All detailed considerations given
for various 4-point Green functions are easily generizable to higher functions.Comment: In Revtex, 12 pages + 2 PostScript figure
