A variant of Schwarzian mechanics

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Abstract

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. An embedding of the Schwarzian mechanics into a larger dynamical system associated with the geodesics of a Brinkmann-like metric obeying the Einstein equations is constructed.

Original languageEnglish
Pages (from-to)661-667
Number of pages7
JournalNuclear Physics B
Volume936
DOIs
Publication statusPublished - 1 Nov 2018

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dynamical systems
Einstein equations
embedding
equations of motion
formulations
symmetry

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

A variant of Schwarzian mechanics. / Galajinsky, Anton.

In: Nuclear Physics B, Vol. 936, 01.11.2018, p. 661-667.

Research output: Contribution to journalArticle

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