Modification of the effective action approach for the Leggett mode

The modified procedure to get the effective action is discussed. Careful observation of phase of electrons leads to the conclusion that Hubbard-Stratonovich field should be pair wavefunction, instead of gap. The modified theory is valid for arbitrary strong interband coupling while the earlier approach only deals with weak interband coupling. This paper also discusses experimental observation of the Leggett mode: Raman spectroscopy. The spectral peak which corresponds to the Leggett mode is calculated in earlier the earlier and the modified theory, which shows that they are much different.