On the Schwarzian counterparts of conformal mechanics
arXiv:2004.03304
Abstract
It is shown that, if the energy in the Schwarzian mechanics (SM) is equal to the coupling constant in the de Alfaro-Fubini-Furlan (DAFF) model, there exists a link between these two systems. In particular, the equation of motion, SL(2,R)-symmetry transformations and the corresponding conserved charges of SM can be derived from those of the DAFF model by applying a coordinate transformation of a special type, while the general solution of the DAFF system maps to the velocity function of SM. A way to reproduce this link via the method of nonlinear realizations is presented. Schwarzian counterparts of the DAFF mechanics in Newton-Hooke (NH) spacetime as well as a higher derivative generalization of the DAFF model are discussed.
arXiv commentV2: 1+22 pages; typos corrected, minor text improvements, references and acknowledgements added
References in corpus (17)
- Comments on the Sachdev-Ye-Kitaev model
- Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry
- Local scale invariance and strongly anisotropic equilibrium critical systems
- Schrodinger Equations for Higher Order Non-relativistic Particles and N-Galilean Conformal Symmetry
- Remarks on l-conformal extension of the Newton-Hooke algebra
- Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator
- Calogero models and nonlocal conformal transformations
- Dynamical realizations of l-conformal Newton-Hooke group
- AdS_2 Supergravity and Superconformal Quantum Mechanics
- Conformal bridge between asymptotic freedom and confinement
- Schwarzian mechanics via nonlinear realizations
- Dynamical realizations of N=1 l-conformal Galilei superalgebra
- The odd-order Pais-Uhlenbeck oscillator
- Four Lectures on Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics
- Inflationary Cosmology, Diffeomorphism Group of the Line and Virasoro Coadjoint Orbits
- A variant of Schwarzian mechanics
- Higher-derivative generalization of conformal mechanics