A variant of Schwarzian mechanics

Understand

The Schwarzian derivative is invariant under SL(2,R)-transformations and, as thus, any function of it can be used to determine the equation of motion or the Lagrangian density of a higher derivative SL(2,R)-invariant 1d mechanics or the Schwarzian mechanics for short.

• In this note, we consider the simplest variant which results from setting the Schwarzian derivative to be equal to a dimensionful coupling constant.
• It is shown that the corresponding dynamical system in general undergoes stable evolution but for one fixed point solution which is only locally stable.
• Conserved charges associated with the SL(2,R)-symmetry transformations are constructed and a Hamiltonian formulation reproducing them is proposed.