Related papers: Ghost condensation and Ostrogradskian instability …

The Ostrogradski ghost problem that appears in higher derivative system is considered for systems with constraints. A prescription for removal of the ghost creating momenta is described based on the Dirac's constraint analysis. It is shown…

We propose an algebraic analysis using a 3+1 decomposition to identify conditions for a clever cancellation of the higher derivatives, which plagued the theory with Ostrogradsky ghosts, by exploiting some existing degeneracy in the…

We provide a full analysis of ghost free higher derivative field theories with coupled degrees of freedom. Assuming the absence of gauge symmetries, we derive the degeneracy conditions in order to evade the Ostrogradsky ghosts, and analyze…

Higher order derivative theories, generally suffer from instabilities, known as Ostrogradsky instabilities. This issue can be resolved by removing any existing degeneracy present in such theories. We consider a model involving at most…

Newtons second law, Schrodingers equation and Maxwells equations are all theories composed of at most second-time derivatives. Indeed, it is not often we need to take the time derivative of the acceleration. So why are we not seeing more…

We construct no-ghost theories of analytic mechanics involving arbitrary higher-order derivatives in Lagrangian. It has been known that for theories involving at most second-order time derivatives in the Lagrangian, eliminating linear…

Ostrogradsky theorem states that Hamiltonian is unbounded when Euler-Lagrange equations are higher than second-order differential equations under the nondegeneracy assumption. Since higher-order nondegenerate Lagrangian can be always recast…

As the first step to extend our understanding of higher-derivative theories, within the framework of analytic mechanics of point particles, we construct a ghost-free theory involving third-order time derivatives in Lagrangian. While…

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…

We prove that the linear instability in a non-degenerate higher derivative theory, the Ostrogradski instability, can only be removed by the addition of constraints if the original theory's phase space is reduced.

Interacting theories with higher derivatives involve ghosts. They correspond to instabilities that display themselves at the classical level. We notice that comparatively "benign" mechanical higher-derivative systems exist where the…

The Ostrogradsky theorem implies that higher-derivative terms of a single mechanical variable are either trivial or lead to additional, ghost-like degrees of freedom. In this letter we systematically investigate how the introduction of…

Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering "degenerate" Lagrangians, whose kinetic matrix cannot be inverted,…

This contribution reviews scalar-tensor theories whose Lagrangian contains second-order derivatives of a scalar field but nevertheless propagate only one scalar mode (in addition to the usual two tensor modes), and are thus not plagued with…

Ghost fields in quantum field theory have been a long-standing problem. Specifically, theories with higher derivatives involve ghosts that appear in the Hamiltonian in the form of linear momenta term, which is commonly known as the…

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically…

We consider higher-order derivative interactions beyond second-order generalized Proca theories that propagate only the three desired polarizations of a massive vector field besides the two tensor polarizations from gravity. These new…

We review the fate of the Ostrogradsky ghost in higher-order theories. We start by recalling the original Ostrogradsky theorem and illustrate, in the context of classical mechanics, how higher-derivatives Lagrangians lead to unbounded…

Perturbation theory for gravity in dimensions greater than two requires higher derivatives in the free action. Higher derivatives seem to lead to ghosts, states with negative norm. We consider a fourth order scalar field theory and show…

Recently, a generalization of invertible disformal transformations containing higher-order derivatives of a scalar field has been proposed in the context of scalar-tensor theories of gravity. By applying this generalized disformal…