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Healthy degenerate theories with higher derivatives

Abstract : In the context of classical mechanics, we study the conditions under which higher-order derivative theories can evade the so-called Ostrogradsky instability. More precisely, we consider general Lagrangians with second order time derivatives, of the form L(̈phia, dot phia, phia, q(i), q(i)) with a = 1,⋯,n and i = 1,⋯,m. For n = 1, assuming that the qi's form a nondegenerate subsystem, we confirm that the degeneracy of the kinetic matrix eliminates the Ostrogradsky instability. The degeneracy implies, in the Hamiltonian formulation of the theory, the existence of a primary constraint, which generates a secondary constraint, thus eliminating the Ostrogradsky ghost. For n > 1, we show that, in addition to the degeneracy of the kinetic matrix, one needs to impose extra conditions to ensure the presence of a sufficient number of secondary constraints that can eliminate all the Ostrogradsky ghosts. When these conditions that ensure the disappearance of the Ostrogradsky instability are satisfied, we show that the Euler-Lagrange equations, which involve a priori higher order derivatives, can be reduced to a second order system.
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Submitted on : Monday, July 3, 2017 - 5:52:21 PM
Last modification on : Friday, May 22, 2020 - 1:23:22 AM

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Hayato Motohashi, Karim Noui, Teruaki Suyama, Masahide Yamaguchi, David Langlois. Healthy degenerate theories with higher derivatives. JCAP, 2016, 07, pp.033. ⟨10.1088/1475-7516/2016/07/033⟩. ⟨hal-01554346⟩

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