Schwarzian mechanics via nonlinear realizations

Abstract

The method of nonlinear realizations is used to clarify some conceptual and technical issues related to the Schwarzian mechanics. It is shown that the Schwarzian derivative arises naturally, if one applies the method to SL(2,R) times R group and decides to keep the number of the independent Goldstone fields to a minimum. The Schwarzian derivative is linked to the invariant Maurer-Cartan one-forms, which make its SL(2,R)-invariance manifest. A Lagrangian formulation for a variant of the Schwarzian mechanics studied recently in [Nucl. Phys. B 936 (2018) 661] is built and its geometric description in terms of 4d metric of the ultrahyperbolic signature is given.

V2: 9 pages, minor improvements, the version to appear in PLB

References in corpus (2)

• Eisenhart lift for higher derivative systems
• Eisenhart Lift of $2$--Dimensional Mechanics

Cited by in corpus (3)

• Super-Schwarzians via nonlinear realizations
• On the Schwarzian counterparts of conformal mechanics
• $\mathcal{N}=4$ supersymmetric Schwarzian with $D(1,2;\alpha )$ symmetry