Related papers: Ghost-free theories with arbitrary higher-order ti…
The problem of gauge symmetry in higher derivative Lagrangian systems is discussed from a Hamiltonian point of view. The number of independent gauge parameters is shown to be in general {\it{less}} than the number of independent primary…
We present our recent contributions to the theory of Lagrangian descriptors for discriminating ordered and deterministic chaotic trajectories. The class of Lagrangian Descriptors we are dealing with is based on the Euclidean length of the…
Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the…
A discussion of the number of degrees of freedom, and their dynamical properties, in higher-derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of…
A metric transformation is a tool to find a new theory of gravity beyond general relativity. The gravity action is guaranteed to be free from a dangerous Ostrogradsky mode as long as the metric transformation is regular and invertible.…
Linearized four-derivative gravity with a general gauge fixing term is considered. By a Legendre transform and a suitable diagonalization procedure it is cast into a second-order equivalent form where the nature of the physical degrees of…
We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form…
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 perform a helicity decomposition in the full Lagrangian of the class of Massive Gravity theories previously proven to be free of the sixth (ghost) degree of freedom via a Hamiltonian analysis. We demonstrate, both with and without the…
Higher derivative scalar interactions can give rise to interesting cosmological scenarios. We present a complete classification of such operators that can yield sizeable effects without introducing ghosts and, at the same time, define an…
The Hamilton theories for higher orders classical Lagrange functions result on a well known Ostrogradski's instabilities. In this work, we propose a different definition for the second order canonical momentum and obtain a new set of second…
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional scalar variable $z$. This provides a geometric framework for…
New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first order Lagrangian by boundary terms only. A new method of deriving…
Some intrinsic tools from the formal theory of variational equations are being demonstrated at work in application to one concrete example of the third-order evolution equation of free relativistic top in three-dimensional space-time. The…
We address the long-standing ``ghost problem" in higher time-derivative theories (HTDTs), where quantisation typically yields sectors with either unbounded spectra or non-normalisable eigenstates; both rendering the theory unphysical. We…
We propose an exact, analytic deformation of the Starobinsky model governed by the strictly positive derivative of its Lagrangian, $f'(R) = \alpha R + \sqrt{\alpha^2 R^2 + 1}$, with $\alpha > 0$. This geometric hyperbolic square-root ansatz…
We perform the complete canonical analysis of the tetrad formulation of bimetric gravity and confirm that it is ghost-free describing the seven degrees of freedom of a massless and a massive gravitons. In particular, we find explicit…
We derive the most generic Carrollian higher derivative free scalar field theory intrinsically on a Carrollian manifold. The solutions to these theories are massless free particles propagating with speeds depending on the coupling constants…
We show that the strong self-interaction of the scalar polarization of a massive graviton can be understood in terms of the propagation of an extra ghost-like degree of freedom, thus relating strong coupling to the sixth degree of freedom…
We briefly review the formulation of effective field theories (EFTs) in time-dependent situations, with particular attention paid to their domain of validity. Our main interest is the extent to which solutions of the EFT capture the…