In this paper we derive the exact expression of the four-spinon contri
bution to the dynamical correlation function of the spin S = 1/2 aniso
tropic (XXZ) Heisenberg model in the antiferromagnetic regime. We exte
nsively study its isotropic (XXX) limit and derive perturbatively the
Ising one. Our method relies on the quantum affine symmetry of the mod
el, which allows for a systematic diagonalization of the Hamiltonian i
n the thermodynamic limit and for an exact calculation of matrix eleme
nts of local spin operators. In fact, we argue that the familiar criti
cism of this method related to the complication of these matrix elemen
ts is not justified. First, we give, in the form of contour integrals,
an exact expression for the n-spinon contribution. After we compile r
ecently found results concerning the two-spinon contribution, we speci
alize the R-spinon formula to the new case n = 4. Then we give an expl
icit series representation of this contribution in the isotropic limit
. Finally, after we show that this representation is free of divergenc
es, we discuss the Ising limit in which a simple expression is found u
p to first order in the anisotropy parameter. (C) 1997 Elsevier Scienc
e B.V.