  We present a path integral formalism for the intrinsic quantum dynamics of
magnetic skyrmions coupled to a thermal background of magnetic fluctuations.
Upon promoting the skyrmion's collective coordinate $\boldsymbol{R}$ to a
dynamic variable and integrating out the magnonic heat bath, we derive the
generalized equation of motion for $\boldsymbol{R}$ with a non-local damping
term that describes a steady-state skyrmion dynamics at finite temperatures.
Being essentially temperature dependent, the intrinsic damping is shown to
originate from the coupling of thermally activated magnon modes to the
adiabatic potential driven by a rigid skyrmion motion, which can be regarded as
another manifestation of emergent electrodynamics inherent to topological
magnetic textures. We further argue that the diagonal components of the damping
term act as the source of dissipation and inertia, while its off-diagonal
components modify the gyrotropic motion of a magnetic skyrmion. By means of
numerical calculations for the lattice spin model of chiral ferromagnets, we
study the temperature behavior of the intrinsic damping as a function of
magnetic field in periodic and confined geometries. The intrinsic damping is
demonstrated to be highly non-local, revealing its quantum-mechanical nature,
that becomes more pronounced with increasing temperature. At high temperatures
when the magnon occupation factors are large, the intrinsic damping is shown to
yield a modified Thiele's equation with the additional non-local dissipative
and mass terms that exhibit an almost linear temperature behavior. Our results
provide a microscopic background for semiclassical magnetization dynamics and
establish a framework for understanding spin caloritronics effects in
topological magnetic textures.
