Phase Formulation and Exact Solutions for the Relativistic Klein–Gordon Field with a Time-Dependent Hamiltonian**The project supported by National Natural Science Foundation of China, the Foundation for Ph.D. TrainingProgram of China and Zhejiang Provincial Natural Science Foundation of China

Abstract

On the basis of the phase formulation, we find the quantum and classical exact solutions and corresponding total phases for the Klein–Gordon (KG) field with a time-dependent Hamiltonian. The total phase includes both the dynamical and geometric phases (Abaronov–Anandan phase). The connection between the quantum and classical solutions is then obtained. From this connection, we discuss the condition under which the geometric phase for the KG field can be defined.