  The problem of the cosmological constant is considered in the formalism of an
extended space-time consisting of the extended classical solution of Einstein
equations. The different regions of the extended manifold are proposed to be
related by the charge, parity, time and mass (CPTM) reversal symmetry applied
with respect to the metric fields of the manifolds. There are interactions
between the points of the extended manifold provided by scalar fields present
separately in the different patches of the extended solution. The value of the
constant is obtained equal to zero at the classical level due the mutual
contribution of the fields in the vacuum energy, it's non-zero value is due the
quantum interactions between the fields. There are few possible scenario for
the actions of the fields are discussed. Each from the obtained variants is
similar to the closed time path approach of non-equilibrium condensed matter
physics and among these possibilities for the closed paths, there is a variant
of the action equivalent to the formalism of Keldysh. Accordingly, we consider
and shortly discuss the application of the proposed formalism to the problem of
smallness of the cosmological constant and singularities problem.
