HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

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.
Complete list of metadata

Contributor : Inspire Hep Connect in order to contact the contributor
Submitted on : Monday, July 3, 2017 - 5:52:21 PM
Last modification on : Thursday, April 7, 2022 - 1:58:22 PM

Links full text




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⟩



Record views