  Essential properties of semiclassical approximation for quantum mechanics are
viewed as axioms of an abstract semiclassical mechanics. Its symmetry
properties are discussed. Semiclassical systems being invariant under Lie
groups are considered. An infinitesimal analog of group relation is written.
Sufficient conditions for reconstructing semiclassical group transformations
(integrability of representation of Lie algebra) are discussed. The obtained
results may be used for mathematical proof of Poincare invariance of
semiclasical Hamiltonian field theory and for investigation of quantum
anomalies.
