  We formulate symmetries in semiclassical Gaussian wave packet dynamics and
find the corresponding conserved quantities, particularly the semiclassical
angular momentum, via Noether's theorem. We consider two slightly different
formulations of Gaussian wave packet dynamics; one is based on earlier works of
Heller and Hagedorn, and the other based on the symplectic-geometric approach
by Lubich and others. In either case, we reveal the symplectic and Hamiltonian
nature of the dynamics and formulate natural symmetry group actions in the
setting to derive the corresponding conserved quantities (momentum maps). The
semiclassical angular momentum inherits the essential properties of the
classical angular momentum as well as naturally corresponds to the quantum
picture.
