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2019

Schwarzian mechanics via nonlinear realizations

Galajinsky, Anton

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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.

Schwarzian mechanics via nonlinear realizations · Around

Built on

A.P. Fordy, A. Galajinsky, Eisenhart lift of 2–dimensional mechanics
Original
1901
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L. Eisenhart, Dynamical trajectories and geodesics
1929
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S.R. Coleman, J. Wess, B. Zumino, Structure of phenomenological Lagrangians. I
1969
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V. de Alfaro, S. Fubini, G. Furlan, Conformal invariance in quantum mechanics
1976
Earlier work this paper cites.

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Then

G.W. Gibbons, T. Houri, D. Kubiznak, C. Warnick, Some spacetimes with higher rank Killing–Stackel tensors
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T.G. Mertens, G.J. Turiaci, H.L. Verlinde, Solving the Schwarzian via the conformal bootstrap
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A. Galajinsky, I. Masterov, Eisenhart lift for higher derivative systems
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A. Galajinsky, A variant of Schwarzian mechanics
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