  The Green's function for a hole moving in an antiferromagnet is derived
analytically in the long-wavelength limit. We find that the infrared divergence
is eliminated in two and higher dimensions so that the quasiparticle weight is
finite. Our results also suggest that the hole motion is polaronic in nature
with a bandwidth proportional to $t/J \exp [-c (t/J)^2] $ ($c$ is a constant).
The connection of the long-wavelength approximation to the first-order
approximation in the cumulant expansion is also clarified.
