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 |
|---|---|
| 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 |
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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.
In: Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, Vol. 795, 10.08.2019, p. 277-280.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 -