On the instability of classical dynamics in theories with higher derivatives

Abstract

The development of instability in the dynamics of theories with higher derivatives is traced in detail in the framework of the Pais-Uhlenbeck fourth oder oscillator. For this aim the external friction force is introduced in the model and the relevant solutions to equations of motion are investigated. As a result, the physical implication of the energy unboundness from below in theories under consideration is revealed.

arXiv comment9 pages, no figures and no tables, revtex4; a few misprints are corrected

References in corpus (8)

• Living with Ghosts
• Benign vs malicious ghosts in higher-derivative theories
• Dirac Quantization of the Pais-Uhlenbeck Fourth Order Oscillator
• Ghost-free higher-derivative theory
• Cosmic acceleration as the solution to the cosmological constant problem
• Is it possible to assign physical meaning to field theory with higher derivatives?
• On squaring the primary constraints in a generalized Hamiltonian dynamics
• On the model of the relativistic particle with curvature and torsion

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