Classical and quantum stability of higher-derivative dynamics

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 ti...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2014-10, Vol.74 (10), p.1-19, Article 3072
Main Authors: Kaparulin, D. S., Lyakhovich, S. L., Sharapov, A. A.
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Construction
Dynamical systems
Dynamics
Electrodynamics
Elementary Particles
Hadrons
Heavy Ions
Integrals
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Oscillators
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Regular Article - Theoretical Physics
Scalars
Stability
String Theory
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Summary: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 they keep the system stable.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-014-3072-3