Schwarzian mechanics via nonlinear realizations

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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)×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 A. Galajinsky (2018) [5] is built and its geometric description in terms of 4d metric of the ultrahyperbolic signature is given.

Original languageEnglish
Pages (from-to)277-280
Number of pages4
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume795
DOIs
Publication statusPublished - 10 Aug 2019

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Keywords

  • Schwarzian mechanics
  • The method of nonlinear realizations

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

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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)×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 A. Galajinsky (2018) [5] is built and its geometric description in terms of 4d metric of the ultrahyperbolic signature is given.",
keywords = "Schwarzian mechanics, The method of nonlinear realizations",
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AB - 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)×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 A. Galajinsky (2018) [5] is built and its geometric description in terms of 4d metric of the ultrahyperbolic signature is given.

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