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Abstract
It is shown that, if the energy in the Schwarzian mechanics (SM) is equal to the coupling constant in the de Alfaro-Fubini-Furlan (dAFF) model, there exists a link between these two systems. In particular, the equation of motion, sl(2,R)-symmetry transformations and the corresponding conserved charges of SM can be derived from those of dAFF model by applying a coordinate transformation of a special type, while the general solution of dAFF system maps to the velocity function of SM. It is also demonstrated that the Hamiltonian of SM can be obtained from the Hamiltonian of dAFF model by applying coupling-constant metamorphosis and the oxidation procedure.
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