Dynamic and kinematic interaction of magnons in an antiferromagnet

The Hamiltonian of the spin system of an antiferromagnet with magnetic anisotropy of easy axis type is quantized on the basis of the representation of the spin operators in terms of creation and annihilation operators for true and fictitious magnons. The properties of the magnon interaction amplitudes are investigated, and it is shown that the approach employed, in the framework of which the contribution of the unphysical states can be readily eliminated at arbitrary temperatures, is self-consistent. It is shown that at low temperatures the effects of the kinematic interaction of the magnons in the antiferromagnet are suppressed exponentially compared with the effects of the dynamic interaction.