# Quantizing with a Higher Time Derivative

@article{Ketov2012QuantizingWA, title={Quantizing with a Higher Time Derivative}, author={Sergei Ketov and Genta Michiaki and Tsukasa Yumibayashi}, journal={arXiv: High Energy Physics - Theory}, year={2012} }

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

#### 11 Citations

Classical and Quantum Dynamics of Higher-Derivative Systems

- Physics
- 2017

A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and… Expand

Quantum mechanics of 4-derivative theories

- Physics, Medicine
- The European physical journal. C, Particles and fields
- 2016

A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton admits a sensible quantization, and the resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. Expand

Classical and quantum stability of higher-derivative dynamics

- Physics, Mathematics
- 2014

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… Expand

Time dependent Pais-Uhlenbeck oscillator and its decomposition

- Physics
- 2015

The Pais-Uhlenbeck(PU) oscillator is the simplest model with higher time derivatives. Its properties were studied for a long time. In this paper, we extend the 4th order free PU oscillator to a more… Expand

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

- Physics
- The European Physical Journal C
- 2019

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… Expand

Higher time derivatives in the microcanonical ensemble describe dynamics of flux-coupled classical and quantum oscillators

- Physics, Mathematics
- 2018

We show that it is possible to consistently describe dynamical systems, whose equations of motion are of degree higher than two, in the microcanonical ensemble, even if the higher derivatives aren't… Expand

New actions for modified gravity and supergravity

- Physics
- 2013

A bstractWe 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 ($ \mathcal{R} $) and… Expand

MODIFIED SUPERGRAVITY AND EARLY UNIVERSE: THE MEETING POINT OF COSMOLOGY AND HIGH-ENERGY PHYSICS

- Physics
- 2012

We review the new theory of modified supergravity, dubbed the supergravity, and some of its recent applications to inflation and reheating in the early universe cosmology. The supergravity is the N =… Expand

Inflation and nonminimal scalar-curvature coupling in gravity and supergravity

- Physics
- 2012

Inflationary slow-roll dynamics in Einstein gravity with a nonminimal scalar-curvature coupling can be equivalent to that in the certain f(R) gravity theory. We review the correspondence and extend… Expand

Cosmological constant in F(R) supergravity

- Physics
- 2011

A cosmological constant in the regime of low space–time curvature is calculated in the recently proposed version of F(R) supergravity with a generic cubic function F. The F(R) supergravity is the N=1… Expand

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