  In this paper we derive the exact expression of the four-spinon contribution
to the dynamical correlation function of the spin S= 1/2 anisotropic (XXZ)
Heisenberg model in the antiferromagnetic regime. We extensively study its
isotropic (XXX) limit and derive perturbatively the Ising one. Our method
relies on the quantum affine symmetry of the model, which allows for a
systematic diagonalization of the Hamiltonian in the thermodynamic limit and
for an exact calculation of matrix elements of local spin operators. In fact,
we argue that the familiar criticism of this method related to the complication
of these matrix elements is not justified. First, we give, in the form of
contour integrals, an exact expression for the n-spinon contribution. After we
compile recently found results concerning the two-spinon contribution, we
specialize the n-spinon formula to the new case n=4. Then we give an explicit
series representation of this contribution in the isotropic limit. Finally,
after we show that this representation is free of divergences, we discuss the
Ising limit in which a simple expression is found up to first order in the
anisotropy parameter.
