  The analysis of geometric phases is briefly reviewed by emphasizing various
gauge symmetries involved. The analysis of geometric phases associated with
level crossing is reduced to the familiar diagonalization of the Hamiltonian in
the second quantized formulation. A hidden local gauge symmetry becomes
explicit in this formulation and specifies physical observables; the choice of
a basis set which specifies the coordinates in the functional space is
arbitrary in the second quantization, and a sub-class of coordinate
transformations, which keeps the form of the action invariant, is recognized as
the gauge symmetry. It is shown that the hidden local symmetry provides a basic
concept which replaces the notions of parallel transport and holonomy. We also
point out that our hidden local gauge symmetry is quite different from a gauge
symmetry used by Aharonov and Anandan in their definition of non-adiabatic
phases.
