Quantizing with a higher time derivative

Ketov, Sergei V.; Genta, Michiaki,; Yumibayashi, Tsukasa

doi:10.48550/arxiv.1110.1155

Cited by 5 publications

(5 citation statements)

References 20 publications

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“…and where the P-U coefficients η i can be found in [31] and in (13). Note that the frequencies ω k are the roots of the polynomial equation p(ω k ) = 0, see (8).…”

Section: Arbitrary Nmentioning

confidence: 99%

Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants

et al. 2019

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The status of classical stability in higher-derivative systems is still subject to discussions. In this note, we argue that, contrary to general belief, many higher-derivative systems are classically stable. The main tool to see this property are Nekhoroshev's estimates relying on the action-angle formulation of classical mechanics. The latter formulation can be reached provided the Hamiltonian is separable, which is the case for higher-derivative harmonic oscillators. The Pais-Uhlenbeck oscillators appear to be the only type of higher-derivative harmonic oscillator with stable classical dynamics. A wide class of interaction potentials can even be added that preserve classical stability. Adiabatic invariants are built in the case of a Pais-Uhlenbeck oscillator slowly changing in time; it is shown indeed that the dynamical stability is not jeopardised by the time-dependent perturbation. arXiv:1811.07733v2 [physics.class-ph]

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“…and where the P-U coefficients η i can be found in [31] and in (13). Note that the frequencies ω k are the roots of the polynomial equation p(ω k ) = 0, see (8).…”

Section: Arbitrary Nmentioning

confidence: 99%

Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants

et al. 2019

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“…The Hamiltonians H α,β are derived from E α,β by substitution φ, φ, φ, ... φ in terms of the phase-space variables (20). The Ostrogradsky Hamiltonian and bracket correspond to α = 1, β = −1:…”

Section: Stability Of the Pais-uhlenbeck Oscillatormentioning

confidence: 99%

Classical and quantum stability of higher-derivative dynamics

2014

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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, higherderivative 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.

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“…Due to the presence of the C2 term in the action (21), this quantum gravity theory is formally renormalizable but has ghosts in Minkowski background [6]. In the context of a fundamental theory of quantum gravity any presence of ghosts is unacceptable [35] so that the C 2 term may not be allowed. However, in the perturbative framework, when the gravity spectrum is determined by the leading (Einstein-Hilbert) action while all the other higher-derivative terms are considered as the interaction, the presence of the C2 term is not a problem.…”

Section: F (R C) Gravity In Einstein Framementioning

confidence: 99%

New actions for modified gravity and supergravity

Ketov

Terada

2013

J. High Energ. Phys.

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We extend the f (R) gravity action by including a generic dependence upon the Weyl tensor, and further generalize it to supergravity by using the super-curvature (R) and super-Weyl (W) chiral superfields in N = 1 chiral curved superspace. We argue that our (super)gravitational actions are the meaningful extensions of the phenomenological f (R) gravity and its locally supersymmetric generalization towards their UV completion and their embedding into superstring theories. The proposed actions can be used for study of cosmological perturbations and gravitational instabilities due to a nonvanishing Weyl tensor in gravity and supergravity.

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Quantizing with a higher time derivative

Abstract: We review the classical and quantum theory of the Pais-Uhlenbeck oscillator as the toy-model for quantizing f (R) gravity theories.

Cited by 5 publications

References 20 publications

Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants

Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants

Classical and quantum stability of higher-derivative dynamics

New actions for modified gravity and supergravity

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