Hidden symmetries from distortions of the conformal structure

Dimakis, N.

doi:10.1103/physrevd.106.024043

Cited by 4 publications

(1 citation statement)

References 84 publications

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“…In this case, one finds the conditional QFIs which are non-local QFIs, that is, they contain quantities within integrals. This is the type of FIs given, e.g., in [21,22,23].…”

Section: The Direct Approachmentioning

confidence: 99%

Quadratic First Integrals of Constrained Autonomous Conservative Dynamical Systems with Fixed Energy

Mitsopoulos

Tsamparlis

2022

Symmetry

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We consider autonomous conservative dynamical systems which are constrained with the condition that the total energy of the system has a specified value. We prove a theorem which provides the quadratic first integrals (QFIs), time-dependent and autonomous, of these systems in terms of the symmetries (conformal Killing vectors and conformal Killing tensors) of the kinetic metric. It is proved that there are three types of QFIs and for each type we give explicit formulae for their computation. It is also shown that when the autonomous QFIs are considered, then we recover the known results of previous works. For a zero potential function, we have the case of constrained geodesics and obtain formulae to compute their QFIs. The theorem is applied in two cases. In the first case, we determine potentials which admit the second of the three types of QFIs. We recover a superintegrable potential of the Ermakov type and a new integrable potential whose trajectories for zero energy and zero QFI are circles. In the second case, we integrate the constrained geodesic equations for a family of two-dimensional conformally flat metrics.

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“…In this case, one finds the conditional QFIs which are non-local QFIs, that is, they contain quantities within integrals. This is the type of FIs given, e.g., in [21,22,23].…”

Section: The Direct Approachmentioning

confidence: 99%

Quadratic First Integrals of Constrained Autonomous Conservative Dynamical Systems with Fixed Energy

Mitsopoulos

Tsamparlis

2022

Symmetry

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Various disguises of the Pais-Uhlenbeck oscillator

Elbistan

Andrzejewski

2023

Nuclear Physics B

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Observational constraints on two cosmological models of f(Q) theory

Koussour

2023

Eur. Phys. J. C

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In the past few years, f(Q) theories have drawn a lot of research attention in replacing Einstein’s theory of gravity successfully. The current study examines the novel cosmological possibilities emerging from two specific classes of f(Q) models using the parametrization form of the equation of state (EoS) parameter as $$\omega \left( z\right) =-\frac{1}{1+3\beta \left( 1+z\right) ^{3}}$$ ω z = - 1 1 + 3 β 1 + z 3 , which displays quintessence behavior with the evolution of the Universe. We do statistical analyses using the Markov chain Monte Carlo (MCMC) method and background datasets like Type Ia Supernovae (SNe Ia) luminosities and direct Hubble datasets (from cosmic clocks), and Baryon Acoustic Oscillations (BAO) datasets. This lets us compare these new ideas about the Universe to the $$\Lambda $$ Λ CDM model in a number of different possible ways. We have come to the conclusion that, at the current level of accuracy, the values of their specific parameters are the best fits for our f(Q) models. To conclude the accelerating behavior of the Universe, we further study the evolution of energy density, pressure, and deceleration parameter for these f(Q) models.

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Hidden symmetries from distortions of the conformal structure

Cited by 4 publications

References 84 publications

Quadratic First Integrals of Constrained Autonomous Conservative Dynamical Systems with Fixed Energy

Quadratic First Integrals of Constrained Autonomous Conservative Dynamical Systems with Fixed Energy

Various disguises of the Pais-Uhlenbeck oscillator

Observational constraints on two cosmological models of f(Q) theory

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