Dynamical symmetry and geometric phase

By considering dynamical symmetry between canonically equivalent systems, we investigate the connection between the geometric phase and dynamical invariants, where the Liouville-von-Neumann equation is directly deduced. Furthermore, we show that an arbitrary shift of the Hamiltonian H(t) → H'(t) = H(t) + Σifi(t)Xi, where fi(t) is a real function and Xi is a generator of dynamical symmetry, leaves the geometric phase invariant