Topological field theory of dynamical systems. II

Ovchinnikov, Igor V.
March 2013
Chaos;Mar2013, Vol. 23 Issue 1, p013108
Academic Journal
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)F⁁, where F⁁ 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.


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