ADIABATIC SPECTRAL FLOW AND CHANGE OF MORSE INDEXES

The concept of the Morse index characterizes the behavior near the cri tical points of the action functional that governs physical systems. W e study the specific feature of Morse indices for the case that there are several number of critical points; on each of these critical point s the Morse indices are defined. As a concrete example, we consider a model of one-dimensional field theory model. By using the idea of the adiabatic spectral flow, it is shown that the change of the Morse indi ces is correlated with the structure change inherent in the solutions of field equation that is controlled by the parameters built in the fi eld action.