Collective Modes in the TRSB Phase of Multiband Superconductors

We develop a theory for the oscillation modes of the order parameters in multiband superconductors in which all the superconducting gaps cannot be real numbers (TRSB phase) and calculate the correlation functions for the amplitude and phase modes. The vertex functions arising from the scattering between electrons and the collective modes are determined so as to satisfy the Ward-Takahashi identity. It is also shown that the multiple amplitude modes appear in the region near the pair-breaking threshold energies.