}^{\dagger }(t^{\prime })\}\rangle .$$

The Dyson’s equation for $G({\bf k},\omega )$ has the form $$\label{dy}G^{-1}({\bf k},\omega )=G_0^{-1}-\Sigma ({\bf k},\omega ),\Sigma (
{\bf k},\omega )=\langle {\cal R}_{{\bf k},\sigma }|{\cal R}_{{\bf k},\sigma
}^{\dagger }\rangle ^{(irr)},$$ where $$G_0=(\omega -\Omega _{{\bf k}})^{-1},{\cal R}_{{\bf k},\sigma }=[{\cal B}_{
{\bf k},\sigma },\hat H]=\frac 1{\sqrt{NK_{{\bf k}}}}\sum_{{\bf r}}{\rm e}
^{-\imath {\bf k\cdot r}}{\cal R}_{{\bf r},\sigma },$$ $$\label{bdot}{\cal R}_{{\bf r},\sigma }=-4\tau {\cal B}_{{\bf r},\sigma }+
{\cal R}_{{\bf r},\sigma }^\tau +{\cal R}_{{\bf r},\sigma }^J,$$ $${\cal R}_{{\bf r},\sigma }^\tau =-\frac \tau 2\sigma \left( \sum_{{\bf g},
{\bf a},\sigma _1}\sigma _1Z_{{\bf r}}^{\bar \sigma \sigma _1}c_{{\bf r}+
{\bf g}+{\bf a},\bar \sigma _1}-\sum_{{\bf g},{\bf a},\sigma _1,\sigma
_2}\sigma _2Z_{{\bf r}}^{\bar \sigma \sigma _1}Z_{{\bf r}+{\bf g}}^{\sigma
_1\sigma _2}c_{{\bf r}+{\bf g}+{\bf a},\bar \sigma _2}\right) ,$$ $${\cal R}_{{\bf r},\sigma }^J=\frac J4\sigma \left( \sum_{{\bf g},{\bf a}
,\sigma _1}\sigma _1(Z_{{\bf r}}^{\bar \sigma \sigma _2}Z_{{\bf r}+{\bf g}
}^{\sigma _2\bar \sigma _1}-Z_{{\bf r}+{\bf g}}^{\bar \sigma \sigma _2}Z_{
{\bf r}}^{\sigma _2\bar \sigma _1})c_{{\bf r}+{\bf a},\sigma _1}\right) ,$$ $$\label{omk}\Omega _{{\bf k}}=\langle \{{\cal R}_{{\bf k},\sigma },{\cal B}_{
{\bf k},\sigma }^{\dagger }\}\rangle =(\tau Q_\tau +JQ_J)/K_{{\bf k}},$$ $$Q_\tau ({\bf k})=-\frac 72-8\left( \frac 14+C_{{\bf g}}\right) \gamma _{{\bf
k}}+\left( \frac 18-C_{{\bf g}}+\frac 12C_{2{\bf g}}\right) \gamma _{2{\bf k}
}+2\left( \frac 18-C_{{\bf g}}+\frac 12C_{{\bf d}}\right) \gamma _{{\bf dk}
},$$ $$Q_J({\bf k})=C_{{\bf g}}(\gamma _{{\bf 