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Third order equations of motion and the Ostrogradsky instability · Around

2014

Third order equations of motion and the Ostrogradsky instability

Motohashi, Hayato, Suyama, Teruaki

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It is known that any nondegenerate Lagrangian containing time derivative terms higher than first order suffers from the Ostrogradsky instability, pathological excitation of positive and negative energy degrees of freedom.

We show that, within the framework of analytical mechanics of point particles, any Lagrangian for third order equations of motion, which evades the nondegeneracy condition, still leads to the Ostrogradsky instability.
Extension to the case of higher odd order equations of motion is also considered.

Built on

Whittaker., A Treatise on the analytical dynamics of particles and rigid bodies, fourth edition, p.265 (Cambridge University Press, London, 1937)
1937
Earlier work this paper cites.
A. Pais and G. Uhlenbeck, Phys.Rev. 79
1950
Earlier work this paper cites.
P. A. M. Dirac, Can.J.Math. 2
1950
Earlier work this paper cites.
P. A. M. Dirac, Proc.Roy.Soc.Lond. A246
1958
Earlier work this paper cites.
P. A. M. Dirac, Lectures on Quantum Mechanics (Belfer Graduate School of Science, New York, 1964)
1964
Earlier work this paper cites.
G. W. Horndeski, Int.J.Theor.Phys. 10
1974
Earlier work this paper cites.
M. Plyushchay, Mod.Phys.Lett. A3
1988
Earlier work this paper cites.

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