Related papers: Ghost-free theories with arbitrary higher-order ti…
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…
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 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…
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…
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…
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…
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…
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…
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,…
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…
We show a new class of interaction terms with higher derivatives that can be added to every low derivative real scalar, such that the theory is degenerate, and the equation of motion remains of second order. In contrast to previous setups,…
We present an example of the quantum system with higher derivatives in the Lagrangian, which is ghost-free: the spectrum of the Hamiltonian is bounded from below and unitarity is preserved.
We consider, in Minkowski spacetime, higher-order Maxwell Lagrangians with terms quadratic in the derivatives of the field strength tensor, and study their degrees of freedom. Using a 3+1 decomposition of these Lagrangians, we extract the…
A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually…
We perform a Hamiltonian analysis and prove that a large class of scalar-tensor theories whose Lagrangian is given by a generic function $F\left(K_{ab},N,R_{ab},h^{ab},\nabla_a,t\right)$ is free from the Ostrogradsky ghost, and thus these…
We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian…
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…
We systematically construct ghost-free scalar-tensor theories whose Lagrangian includes up to third-order derivatives of the scalar field. Using a spatially covariant action written in terms of the ADM variables, we impose degeneracy and…
Generic higher derivative theories are believed to be fundamentally unphysical because they contain Ostrogradsky ghosts. We show that within complex classical mechanics it is possible to construct higher derivative theories that circumvent…
The Ostrogradsky theorem states that any classical Lagrangian that contains time derivatives higher than the first order and is nondegenerate with respect to the highest-order derivatives leads to an unbounded Hamiltonian which linearly…