Mean field theory for the time evolution of quantum meson fields is studied
in terms of the functional Schroedinger picture with a time-dependent Gaussian
variational wave functional. We first show that the equations of motion for the
variational wavefunctional can be rewritten in a compact form similar to the
Hartree-Bogoliubov equations in quantum many-body theory and this result is
used to recover the covariance of the theory. We then apply this method to the
O(N) model and present analytic solutions of the mean field evolution equations
for an N-component scalar field. These solutions correspond to quantum
rotations in isospin space and represent generalizations of the classical
solutions obtained earlier by Anselm and Ryskin. As compared to classical
solutions new effects arise because of the coupling between the average value
of the field and its quantum fluctuations. We show how to generalize these
solutions to the case of mean field dynamics at finite temperature. The
relevance of these solutions for the observation of a coherent collective state
or a disoriented chiral condensate in ultra-relativistic nuclear collisions is
discussed.Comment: 31 pages, 2 Postscript figures, uses ptptex.st