Polar Decomposition of the Wiener Measure: Schwarzian Theory Versus Conformal Quantum Mechanics

Аннотация

We find an explicit form of the polar decomposition of the Wiener measure and obtain an equation relating functional integrals in conformai quantum mechanics to functional integrals in the Schwarzian theory. Using this relation, we evaluate some nontrivial functional integrals in the Schwarzian theory and also find the fundamental solution of the Schrödinger equation in imaginary time in the model of conformal quantum mechanics.