Effective action and collective bose-excitations in the $t$-$J$-model

The two-dimensional ($2D$) $t$-$T$-model is investigated using the functional integration method. The effective action is obtained, and the spectrum of collective Bose-excitations in the superconductive phase of the system is calculated both in the phase-transition vicinity (Ginsburg–Landau region $|T-T_c|\ll T_c$) and in the low-temperature region $T\ll T_c$. Bibliography: 26 titles.