Quantizing with a Higher Time Derivative

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

doi:10.5772/39048

Cited by 4 publications

References 2 publications

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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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New actions for modified gravity and supergravity

Ketov

Terada

2013

J. High Energ. Phys.

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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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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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Quantizing with a Higher Time Derivative

Cited by 4 publications

References 2 publications

New actions for modified gravity and supergravity

New actions for modified gravity and supergravity

Classical and quantum stability of higher-derivative dynamics

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

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