Classical and quantum stability of higher-derivative dynamics

Abstract

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 keep the system stable.

39 pages, minor corrections, references added

References in corpus (39)

• f(R) Theories Of Gravity
• f(R) theories
• Conditions for the cosmological viability of f(R) dark energy models
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• The stability of modified gravity models
• B-Inflation
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Higher derivative theories with constraints : Exorcising Ostrogradski's Ghost
• Benign vs malicious ghosts in higher-derivative theories
• On Higher Derivatives in 3D Gravity and Higher Spin Gauge Theories
• Bosonic conformal higher--spin fields of any symmetry
• Lagrange structure and quantization
• Higher Derivative Chern--Simons Extensions
• BRST theory without Hamiltonian and Lagrangian
• Stable Self-Interacting Pais-Uhlenbeck Oscillator
• Comments on the Dynamics of the Pais-Uhlenbeck Oscillator
• A Hamiltonian Formulation of the Pais-Uhlenbeck Oscillator that Yields a Stable and Unitary Quantum System
• Path Integral Quantization of Generalized Quantum Electrodynamics
• A Poincare lemma for sigma models of AKSZ type
• Arbitrary spin conformal fields in (A)dS
• Consistent interactions and involution
• A note on higher-derivative actions for free higher-spin fields
• Renormalizability of generalized quantum electrodynamics
• Giving up the ghost
• Rigid Symmetries and Conservation Laws in Non-Lagrangian Field Theory
• Pais-Uhlenbeck Oscillator with a Benign Friction Force
• A spin-4 analog of 3D massive gravity
• On the gauge symmetries of Maxwell-like higher-spin Lagrangians
• Generalised connections and higher-spin equations
• Schwinger-Dyson equation for non-Lagrangian field theory
• Supersymmetric field theory with benign ghosts
• Remarks on quantization of Pais-Uhlenbeck oscillators
• Quantizing non-Lagrangian gauge theories: an augmentation method
• Batalin-Fradkin-Vilkovisky quantization of the generalized scalar electrodynamics
• BRST analysis of general mechanical systems
• Hamiltonian structures for Pais-Uhlenbeck oscillator
• Local BRST cohomology in (non-)Lagrangian field theory
• Higher-derivative massive actions from dimensional reduction
• Canonical formalism and quantization of perturbative sector of higher-derivative theories

Cited by in corpus (66)

• Quadratic Gravity
• Dimensional Transmutation in Gravity and Cosmology
• Pais-Uhlenbeck Oscillator and Negative Energies
• Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom
• Hamilton-Jacobi formalism for Podolsky's electromagnetic theory on the null-plane
• Bopp-Podolsky black holes and the no-hair theorem
• Basic introduction to higher-spin theories
• de Broglie-Proca and Bopp-Podolsky massive photon gases in cosmology
• Normalizability analysis of the generalized quantum electrodynamics from the causal point of view
• Hamiltonian formalisms and symmetries of the Pais-Uhlenbeck oscillator
• An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator
• Higher derivative extensions of $3d$ Chern-Simons models: conservation laws and stability
• Stable interactions in higher derivative field theories of derived type
• Reduction of order and Fadeev-Jackiw formalism in generalized electrodynamics
• A Conducting surface in Lee-Wick electrodynamics
• Scalar-multi-tensorial equivalence for higher order $f\left(R,{\nabla }_{\mu }R,{\nabla }_{{\mu }_1}{\nabla }_{{\mu }_2}R,...,{\nabla }_{{\mu }_1}...{\nabla }_{{\mu }_n}R\right)$ theories of gravity
• Multi-Hamiltonian formulations and stability of higher-derivative extensions of $3d$ Chern-Simons
• A perturbation theory approach to the stability of the Pais-Uhlenbeck oscillator
• Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants
• Stable interactions via proper deformations
• $f\left(R,{\nabla }_{{\mu }_1}R,\dots ,{\nabla }_{{\mu }_1}\dots {\nabla }_{{\mu }_n}R\right)$ theories of gravity in Einstein frame: A higher order modified Starobinsky inflation model in the Palatini approach
• Foundations of ghost stability
• The odd-order Pais-Uhlenbeck oscillator
• BRST symmetry and fictitious parameters
• Resonance and stability of higher derivative theories of derived type
• Stable interactions between the extended Chern-Simons theory and a charged scalar field with higher derivatives: Hamiltonian formalism
• Conservation Laws and Stability of Field Theories of Derived Type
• Asymptotic nonlocality in non-Abelian gauge theories
• Reduced Order Podolsky Model
• Remark on higher-derivative mechanics with l-conformal Galilei symmetry
• Viable wormhole solution in Bopp-Podolsky electrodynamics
• Geometrical structure of Weyl invariants for spin three gauge field in general gravitational background in $d=4$
• Boost invariant regulator for field theories
• Higher time-derivative theories from space-time interchanged integrable field theories
• Peierls brackets in non-Lagrangian field theory
• Conservation laws and stability of higher derivative extended Chern-Simons
• Stability in the higher derivative Abelian gauge field theory
• Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
• Stability and causality of multi-local theories
• Dirichlet boundary condition for the Lee-Wick-like scalar model
• Stable interactions between higher derivative extended Chern-Simons and charged scalar field
• Transition amplitude, partition function and the role of physical degrees of freedom in gauge theories
• Some optical properties of rotating wormhole in Bopp-Podolsky electrodynamics
• General method for including Stueckelberg fields
• Generalized Niederer's transformation for quantum Pais-Uhlenbeck oscillator
• Stability and consistent interactions in Podolsky's generalized electrodynamics
• Third order extensions of $3d$ Chern-Simons interacting to gravity: Hamiltonian formalism and stability
• Superfield approach to higher derivative N=1 superconformal mechanics
• Dualisation of free fields
• Nonlinear evolution of disturbances in higher time-derivative theories
• Path Integral Quantization of Generalized Stueckelberg Electrodynamics: A Faddeev-Jackiw Approach
• Nonlocal dynamics and infinite non-relativistic conformal symmetries
• Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation
• Markov constant and quantum instabilities
• Vacuum Polarization of Generalized Quantum Electrodynamics in the Heisenberg Picture
• Conformal symmetry in damped Pais-Uhlenbeck oscillator
• Generalized quantum electrodynamics: one-loop correction
• N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator
• Environmental gravitational decoherence with higher derivative theory
• Generalized Yang-Mills Theory under Rotor Mechanism
• Symplectic approach to global stability
• A New Perspective on Quantum Field Theory Revealing Possible Existence of Another Kind of Fermions Forming Dark Matter
• Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture
• Calculations in induced gravity from higher-derivative field theories
• Gauss-Bonnet Gravity and Spacetime Singularities
• Møller scattering in $2+1$ of generalized quantum electrodynamics in the heisenberg picture