title: Topological field theory of dynamical systems. II.
abstract: 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.
authors.affiliation: Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, California 90095-1594, USA. iovchinnikov@ucla.edu
authors.forename: Igor V
authors.initials: IV
authors.lastname: Ovchinnikov
mesh_terms: D003198:Computer Simulation; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D011336:Probability; D013269:Stochastic Processes; D013598:Systems Theory; D013997:Time Factors