Trace formulae for stochastic evolution operators: smooth conjugation method

The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighbourhood of a given saddlepoint exactly by means of a smooth conjugacy, a locally analytic nonlinear change of field variables. The perturbative corrections are transferred to the corresponding Jacobian, which we expand in terms of the conjugating function, rather than the action used in defining the path integral. The new perturbative expansion which follows by a recursive evaluation of derivatives appears more compact than the standard Feynman diagram perturbation theory. The result is a stochastic analogue of the Gutzwiller trace formula with the ‘h̄’ corrections computed an order higher than what has so far been attainable in stochastic and quantum mechanical applications. PACS numbers: 0250, 0320, 0365, 0540, 0545 AMS classification scheme number: 58F20