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An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian…

We calculate the cubic order terms in a covariant theory that gives a nonlinear completion of the Fierz-Pauli massive spin-2 action. The resulting terms have specially tuned coefficients guarantying the absence of a ghost at this order in…

We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…

Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the…

In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a non-relativistic spinless system. This Lagrangian is written as a difference between a function $T$, which represents the…

Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…

Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…

Negative kinetic energies correspond to ghost degrees of freedom, which are potentially of relevance for cosmology, quantum gravity, and high energy physics. We present a novel wide class of stable mechanical systems where a positive energy…

Onsager and Machlup proposed a second order variational-principle in order to include inertial effects into the Langevin-equation, giving a Lagrangian with second order derivatives in time. This but violates Ostrogradysky's theorem, which…

The inclusion of higher derivatives is a necessary condition for a renormalizable or superrenormalizable local theory of quantum gravity. On the other hand, higher derivatives lead to classical instabilities and a loss of unitarity at the…

We propose a new class of higher derivative scalar-tensor theories without the Ostrogradsky's ghost instabilities. The construction of our theory is originally motivated by a scalar field with spacelike gradient, which enables us to fix a…

We perform the Hamiltonian analysis of some form of the non-linear massive gravity action that is formulated in the Stuckelberg formalism. Following seminal analysis performed in arXiv:1203.5283 [hep-th] we find that this theory possesses…

In order to explore some general features of modified theories of gravity which involve higher derivatives and spontaneous Lorentz and/or diffeomorphism symmetry breaking, we study the recently proposed new version of covariant…

We show that if the Lagrangean for a scalar field coupled to General Relativity only contains derivatives, then it is possible to completely deparametrise the theory. This means that 1.Physical observables, i.e. functions which Poisson…

This article reviews scalar-tensor theories characterized by a Lagrangian that, despite the presence of second order derivatives, contain a single scalar degree of freedom. These theories, known as Degenerate Higher-Order Scalar-Tensor…

We consider a classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the…

In this paper we study higher-derivative supersymmetric effective field theories focusing on the systematic procedure for the elimination of ghosts from the spectrum. Particular attention is paid to the auxiliary fields, for which the…

Vector Galileons are ghost-free systems containing higher derivative interactions of vector fields. They break the vector gauge symmetry, and the dynamics of the longitudinal vector polarizations acquire a Galileon symmetry in an…

We classify higher-order Maxwell-Einstein theories linear in the curvature tensor and quadratic in the derivatives of the electromagnetic field strength whose kinetic matrices are degenerate. This provides a generalisation of quadratic…

We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…