  The stability of a single Belavin-Polyakov (BP) skyrmion in isotropic
Heisenberg ferromagnet is studied. Such skyrmion is higher in energy than the
uniform ferromagnetic state and is thus metastable. Starting from the lattice
model in two spatial dimensions and using Maleyev-Dyson representation for spin
operators, we examine the effects of magnon-magnon interaction for two
quantities at $T=0$. First we discuss the self-energy corrections to magnon
energy. Second we analyze the two-particle Green's function and possible bound
states of two magnons. The simplicity of the model makes possible full analytic
treatment of all relevant processes. We found that the magnons remain
well-defined quasiparticles with a finite lifetime. The bound states of two
magnons are suppressed near the skyrmion, although they are not excluded far
away from it. A resonance for the magnons of dilational mode in the vicinity of
BP skyrmion is also found, which leads to a redistribution of the spectral
weight. We conclude that the BP skyrmion as the classical topological object is
not destroyed by quantum fluctuations.
