Classical and quantum stability of higher-derivative dynamics

Understand

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.