Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model

The work gives a consistent and uniform exposition of all known results related to Heisenberg model. The classification of excitations is presented and their scattering is described both in ferromagnetic and the antiferromagnetic cases. It is shown that in the antiferromagnetic case there exists only one excitation with spin 1/2 which is a kink in the following sense: in physical states there is only an even number of kinks-spin waves, therefore they always have an integer spin. Thus, it is shown that the conventional picture of excitations is wrong in the antiferromagnetic case and the spin wave has spin 1/2, matrix is calculated.