Magnon renormalization in the Heisenberg ferromagnet

An analysis of the concept of renormalization of magnons is presented in view of a recently developed Bose expansion of spin operators. The advantages as well as the limitations of this concept are discussed. It is shown how the kinematic interaction becomes crucial in the critical region. In our renormalized magnon picture it turns out that the phase transition of the Heisenberg ferromagnet can be described as a generalized Bose condensation in the "kinematic space". Finally, our formalism is used to calculate the magnetization curve of the Heisenberg ferromagnet, yielding $T_c$ in excellent agreement with high-temperature expansions.