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 stochastic expectation values of a DS must be complemented on the TFT side by $(-1{)}^{\hat{F}}$, where $\hat{F}$ is the ghost number operator. The role of this inclusion is to unfold the natural path-integral representation of the TFT, \emph{i.e.}, the Witten index that equals up to a topological factor 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.

8 pages, 1 figure

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• Non-Abelian Anyons and Topological Quantum Computation
• Dynamical synapses causing self-organized criticality in neural networks
• Supersymmetry and fluctuation relations for currents in closed networks
• Topological field theory of dynamical systems

Cited by in corpus (7)

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