Hamiltonian formalisms and symmetries of the Pais-Uhlenbeck oscillator

Abstract

The study of the symmetry of Pais-Uhlenbeck oscillator initiated in [Nucl. Phys. B 885 (2014) 150] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton-Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory) is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.

Published version

References in corpus (8)

• Non-relativistic conformal symmetries and Newton-Cartan structures
• Classical and quantum stability of higher-derivative dynamics
• Remarks on l-conformal extension of the Newton-Hooke algebra
• On the instability of classical dynamics in theories with higher derivatives
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Cited by in corpus (11)

• Dynamical realizations of N=1 l-conformal Galilei superalgebra
• Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
• $\ell$-oscillators from second-order invariant PDEs of the centrally extended Conformal Galilei Algebras
• Minimal realization of $\ell$-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation
• Remark on higher-derivative mechanics with l-conformal Galilei symmetry
• N=2 supersymmetric Pais-Uhlenbeck oscillator
• New realizations of N=2 l-conformal Newton-Hooke superalgebra
• Superfield approach to higher derivative N=1 superconformal mechanics
• Hamiltonian consistency of the gravitational constraint algebra under deformations
• N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator
• Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator