PHASE FORMULATION AND EXACT-SOLUTIONS FOR THE RELATIVISTIC KLEIN-GORDON FIELD WITH A TIME-DEPENDENT HAMILTONIAN

On the basis of the phase formulation, we find the quantum and classic al exact solutions and corresponding total phases for the Klein-Gordon (KG) field with a time-dependent Hamiltonian. The total phase include s both the dynamical and geometric phases (Aharonov-Anandan phase). Th e connection between the quantum and classical solutions is then obtai ned. From this connection, we discuss the condition under which the ge ometric phase for the KG field can be defined.