ИСТИНА

We construct the series of functional integrals in the Schwarzian theory as the integrals on the group of diffeomorphisms. The Schwarzian theory is behind various physical models including the SYK model and the two-dimensional dilaton gravity. A polar decomposition of the Wiener measure based on its quasi-invariance under the group of diffeomorphisms is proposed. As a result, the functional integrals in the Schwarzian theory can be written as Fourier transform of the integrals in a model with the Calogero potential.