Classical and quantum stability of higher-derivative dynamics

Abstract

We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate that the bounded integral of motion is connected with the time-translation invariance. A procedure is suggested for switching on interactions in free higher-derivative systems without breaking their stability. We also demonstrate the quantization technique that keeps the higher-derivative dynamics stable at quantum level. The general construction is illustrated by the examples of the Pais-Uhlenbeck oscillator, higher-derivative scalar field model, and the Podolsky electrodynamics. For all these models, the positive integrals of motion are explicitly constructed and the interactions are included such that keep the system stable.

39 pages, minor corrections, references added

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Cited by in corpus (8)

• Pais-Uhlenbeck Oscillator and Negative Energies
• Hamiltonian formalisms and symmetries of the Pais-Uhlenbeck oscillator
• Stable interactions between the extended Chern-Simons theory and a charged scalar field with higher derivatives: Hamiltonian formalism
• Reduced Order Podolsky Model
• Conservation Laws and Stability of Field Theories of Derived Type
• Remark on higher-derivative mechanics with l-conformal Galilei symmetry
• Peierls brackets in non-Lagrangian field theory
• N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator