Dmitry Kaparulin

Stability of higher derivative dynamics

We observe that a wide class of higher derivative systems admits a bounded conserved quantity that ensures classical stability of the dynamics while the canonical energy is unbounded. We use the tool of Lagrange anchor to demonstrate that bounded integral of motion is connected with the 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 examples of Pais-Uhlenbeck oscillator, higher derivative scalar field model, and higher-derivative Podolsky electrodynamics. For all these models, the positive conserved quantity is explicitly constructed and the interactions are identified such that do not break stability.