Path integral approach to the kinematical Brownian motion due to a random canonical transformation

Summary: "The stochastization of Jacobi's second equality of classical mechanics by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidean quantum theory is obtained. The conditional transition probability density of the presence of a Brownian particle is obtained with the help of the functional integral. The technique of factorization of the solution of the Fokker-Planck equation is employed to evaluate the effective potential energy."