Topological field theory of dynamical systems. II

This paper is a continuation of the study [Chaos.22.033134] of the relation between the stochastic dynamical systems (DS) and the Witten-type topological field theories (TFT). Here, it is discussed that the stochastic expectation values of a DS must be complemented on the TFT side by (-^1)F̂, where F̂ is the ghost number operator. The role of this inclusion is to unfold the natural path-integral representation of the TFT, i.e., the Witten index that equals up to a topological constant to the partition function of the stochastic noise, into the physical partition function of TFT/DS. It is also shown that on the DS side, the TFT's wavefunctions are the conditional probability densities.