  The Schwinger-Keldysh diagram technique is usually involved in the
calculation of real-time in-in correlation functions. In the case of a thermal
state, one can analytically continue imaginary-time Matsubara correlation
functions to real times. Nevertheless, not all real-time correlation functions
usually can be obtained by such procedure. Moreover, numerical analytic
continuation is an ill-posed problem. Thus, even in the case of a thermal state
one may need for the Schwinger-Keldysh formalism. If the potential of a system
admits degenerate minima, instantonic effects enter the game, so one should
also integrate over the instantonic moduli space, including the one,
corresponding to the imaginary time translational invariance. However, the
Schwinger-Keldysh closed time contour explicitly breaks such invariance. We
argue, that this invariance must be recovered, and show, how it can be done.
After that, we construct an extension of the Schwinger-Keldysh diagram
technique to instantonic systems and demonstrate it on the example of the first
few-point correlation functions.
