  We use the two time influence functional method of the path integral approach
in order to reduce the dimension of the coupled-channels equations for
heavy-ion reactions based on the no-Coriolis approximation. Our method is
superior to other methods in that it easily enables us to study the cases where
the initial spin of the colliding particle is not zero. It can also be easily
applied to the cases where the internal degrees of freedom are not necessarily
collective coordinates. We also clarify the underlying assumptions in our
approach.
