### 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 language | English |
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Pages (from-to) | 277-280 |

Number of pages | 4 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 795 |

DOIs | |

Publication status | Published - 10 Aug 2019 |

### Fingerprint

### Keywords

- Schwarzian mechanics
- The method of nonlinear realizations

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Schwarzian mechanics via nonlinear realizations.** / Galajinsky, Anton.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Schwarzian mechanics via nonlinear realizations

AU - Galajinsky, Anton

PY - 2019/8/10

Y1 - 2019/8/10

N2 - 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.

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.

KW - Schwarzian mechanics

KW - The method of nonlinear realizations

UR - http://www.scopus.com/inward/record.url?scp=85067881380&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067881380&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2019.05.054

DO - 10.1016/j.physletb.2019.05.054

M3 - Article

VL - 795

SP - 277

EP - 280

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

ER -