  Semiclassical systems being symmetric under Lie group are studied. A state of
a semiclassical system may be viewed as a set (X,f) of a classical state X and
a quantum state f in the external classical background X. Therefore, the set of
all semiclassical states may be considered as a bundle ("semiclassical
bundle"). Its base {X} is the set of all classical states, while a fibre is a
Hilbert space of quantum states in the external background X. Symmetry
transformation of a semiclassical system may be viewed as an automorphism of
the semiclassical bundle. Automorphism groups can be investigated with the help
of sections of the bundle: to any automorphism of the bundle one assigns a
transformation of section of the bundle. Infinitesimal properties of
transformations of sections are investigated; correspondence between Lie groups
and Lie algebras is discussed. For gauge theories, some points of the
semiclassical bundle are identified: a gauge group acts on the bundle. For this
case, only gauge-invariant sections of the semiclassical bundle are taken into
account.
