integrand. However, because afterwards we take derivative over the fields $A_{\mu}$ and put $A_{\mu}=0$, the only nonzero contribution will come from the part of the integrand linear in $A_{\mu}$. We shall treat the cranking parameter $\Omega \sim {1\over N_c}$ as a small perturbation that is consistent with the large $N_c$ limit philosophy behind the NJL model. Hence, we can neglect terms $\Omega^2$ and higher[^1][Actually, the terms $\sim \Omega^2$ must be taken into account to evaluate the moment of inertia (see \[, \] for details).]{}. Also, we should be careful in performing the ${\cal D}R$ integration, as in general the operators $\hat Q$ and $R$ does not commute and one must use the proper time ordering (see Sect. 4 and \[, \]). In the next step we expand the integrand in () in terms of $A_{\mu}$ and $\Omega$. To this end we apply the Feynman-Schwinger-Dyson (FSD) expansion for the operator exponent:

$$e^{{\cal A}+{\cal B}} = e^{\cal A} +
\int^1_0 d\alpha\,e^{\alpha {\cal A}}\ {\cal B}\ e^{(1-\alpha)
{\cal A}} +
\int^1_0 d\beta\,\int^{1-\beta}_0 d\alpha\,
e^{\alpha {\cal A}}\ {\cal B}\
e^{\beta {\cal A}}\ {\cal B}\
e^{(1-\alpha-\beta) {\cal A}} + ...
\ .\eqno(\OPEXP)$$

In our case, for the operator ${\cal A}$ we substitute the part of 