Some Comments on Ghosts and Unitarity: The Pais-Uhlenbeck Oscillator Revisited

Abstract

We give a simple discussion of ghosts, unitarity violation, negative norm states and quantum vs classical behavior in the simplest model with four derivative action - the Pais-Uhlenbeck oscillator. We also point out that the normalizable "vacuum state" (in the sense defined below) of this model can be understood as spontaneous breaking of the emergent conformal symmetry. We provide an example of an interacting system that couples the "particle" and "ghost" degrees of freedom and nevertheless remains unitary on both classical and quantum level.

arXiv comment14 pages

References in corpus (17)

• Can the dark energy equation-of-state parameter w be less than -1?
• The phantom menaced: constraints on low-energy effective ghosts
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Making the Case for Conformal Gravity
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• Fitting galactic rotation curves with conformal gravity and a global quadratic potential
• Impact of a global quadratic potential on galactic rotation curves
• Dirac Quantization of the Pais-Uhlenbeck Fourth Order Oscillator
• PT symmetry and necessary and sufficient conditions for the reality of energy eigenvalues
• A Symmetry for the Cosmological Constant
• A Hamiltonian Formulation of the Pais-Uhlenbeck Oscillator that Yields a Stable and Unitary Quantum System
• Supersymmetry vs ghosts
• Galactic rotation curves in conformal gravity
• Pais-Uhlenbeck Oscillator with a Benign Friction Force
• Living with ghosts in Lorentz invariant theories
• Imaginary-Scaling versus Indefinite-Metric Quantization of the Pais-Uhlenbeck Oscillator
• Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in UV complete theories with a gravity dual

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• Stable Self-Interacting Pais-Uhlenbeck Oscillator
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• Interpretation of quantum mechanics with indefinite norm
• Pais-Uhlenbeck Oscillator with a Benign Friction Force
• Supersymmetric field theory with benign ghosts
• A perturbation theory approach to the stability of the Pais-Uhlenbeck oscillator
• Dynamical systems with benign ghosts
• Foundations of ghost stability
• On exactly solvable higher-derivative systems
• Holographic Two-Point Functions in Conformal Gravity
• Spontaneous Conformal Symmetry Breaking and Quantum Quadratic Gravity
• Field redefinition invariant Lagrange multiplier formalism
• The Conformal Universe I: Physical and Mathematical Basis of Conformal General Relativity
• Markov constant and quantum instabilities
• Conformal Gravity Redux: Ghost-turned-Tachyon
• A Non-Trivial Zero Length Limit of the Nambu-Goto String
• The Conformal Universe II: Conformal Symmetry, its Spontaneous Breakdown and Higgs Fields in Conformally Flat Spacetime
• The Conformal Universe III: Basic Mechanisms of Matter Generation
• Conformal General Relativity -- Unified Theory of the Standard Models of Elementary Particles and Modern Cosmology