the very basic symbol of the functional integral $$\begin{aligned}
 &&Z=N\int\limits_{{\cal F}} DA \exp\{-S[A]\},
 \end{aligned}$$ where the functional space ${\cal F}$ is subject to the condition $$\begin{aligned}
 \label{cond0}
 {\cal F}=\{A: \lim_{V\to \infty} \frac{1}{V}\int\limits_V d^4xg^2F^a_{\mu\nu} (x)F^a_{\mu\nu}(x) =B_{\mathrm vac}^2\}.\end{aligned}$$ The constant $B_{\mathrm vac}$ is not equal to zero in the general case, which is equivalent to nonzero gluon condensate $\langle g^2F^2 \rangle$. Condition (\[cond0\]) singles out fields $B_\mu^a$ with the strength which is constant almost everywhere in $R^4$. It is a necessary requirement to allow gluon condensate to be nonzero. It does not forbid also fields with a finite action since the case $B_{\mathrm vac}=0$ has to be also studied. The dynamics chooses the value of $B_{\mathrm vac}$. However, the phenomenology of strong interactions has already required nonzero gluon and quark condensates. Hence, they must be allowed in the QCD functional integral from the very beginning. Separation of the long range modes $B_\mu^a$ responsible for gluon condensate and the local fluctuations $Q_\mu^a$ in the background $B_\mu^a$, must be supplemented by the gauge fixing condition. The background gauge condition for fluctuations $D(B)Q=0$ is the most natural choice.

Further steps include integration over the fluctuation fields resulting in the effective action for the long-range fields 