Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator
Copyright policy )Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator
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
- University of Łódź Poland
- Department of Computer Sciences Austria
- Department of Computer Science Spain
- Uniwersytet Łódzki (University of Lodz) Poland
Hamilton's equations, High Energy Physics - Theory, Nuclear and High Energy Physics, FOS: Physical sciences, QC770-798, Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics, Mathematical Physics (math-ph), Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, High Energy Physics - Theory (hep-th), Nuclear and particle physics. Atomic energy. Radioactivity, Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics, Nonlinear resonances for nonlinear problems in mechanics, Mathematical Physics
Hamilton's equations, High Energy Physics - Theory, Nuclear and High Energy Physics, FOS: Physical sciences, QC770-798, Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics, Mathematical Physics (math-ph), Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, High Energy Physics - Theory (hep-th), Nuclear and particle physics. Atomic energy. Radioactivity, Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics, Nonlinear resonances for nonlinear problems in mechanics, Mathematical Physics
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