  We study the effects of quantum fluctuations on excitation spectra in the
two-dimensional Heisenberg antiferromagnet by means of the 1/S expansion. We
calculate the spin-wave dispersion and the transverse dynamical structure
factor up to the second order of 1/S in comparison with inelastic neutron
scattering experiments. The spin-wave energy at momentum $(\pi,0)$ is found to
be about 2% smaller than that at $(\pi/2,\pi/2)$ due to the second-order
correction. In addition, we study the dimensional crossover from two dimensions
to one dimension by weakening exchange couplings in one direction. It is found
that the second-order correction becomes large with approaching the quasi-one
dimensional situation and makes the spin-wave energy approach to the des
Cloizeaux-Pearson boundary for $S=1/2$. The transverse dynamical structure
factor is also calculated up to the second order of 1/S. It is shown that the
intensity of spin-wave peak is strongly reduced while the intensity of
three-spin-wave continuum becomes large and exceeds that of the spin-wave peak
in the quasi-one dimensional situation.
