Related papers: Exorcising the Ostrogradsky ghost in coupled syste…

One of the remarkable differences between renormalizable quantum gravity with four-derivative action and its superrenormalizable polynomial generalizations is that the latter admit a more sophisticated particle mass spectrum. Already in the…

The theory of gravity with an auxiliary extra dimension is known to give the ghost-free cubic completion of the Fierz-Pauli mass term in the decoupling limit. Our work generalizes the boundary condition in the auxiliary dimension that…

We present all scalar-tensor Lagrangians that are cubic in second derivatives of a scalar field, and that are degenerate, hence avoiding Ostrogradsky instabilities. Thanks to the existence of constraints, they propagate no more than three…

In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…

We introduce a method which allows one to recover the equations of motion of a class of nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full phase space, and to restrict the resulting canonical equations…

In this work we develop a theoretical framework for Gauss-Bonnet modified gravity theories, in which ghost modes can be eliminated at the equations of motion level. Particularly, after we present how the ghosts can occur at the level of…

Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel…

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

An equation is obtained to find the Lagrangian for a one-dimensional autonomous system. The continuity of the first derivative of its constant of motion is assumed. This equation is solved for a generic nonconservative autonomous system…

The `classical' model for a massive spinning particle, which was recently proposed, is derived from the isotropic rotator model. Through this derivation, we note that the spin can be understood as the relativistic extension of the isotropic…

In this paper we work out the explicit form of the change of variables that reproduces an arbitrary change of gauge in a higher-order Lagrangian formalism.

We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the fixing of ambiguities in the dynamics and…

We obtain regularity conditions of a new type of problems of the calculus of variations with second-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main result asserts that autonomous integral…

We re-examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather…

With an appropriate choice of parameters, a higher derivative theory of gravity can describe a normal massive sector and a ghost massless sector. We show that, when defined on an asymptotically de Sitter spacetime with Dirichlet boundary…

Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new variational principle to uncover more insights…

When one uses the Dirac bracket, second class constraints become first class. Hence, they are amenable to the BRST treatment characteristic of ordinary first class constraints. This observation is the starting point of a recent…

We perform a Hamiltonian constraint analysis of the multivielbein theory proposed in arXiv:1804.09723. The analysis shows that the secondary constraints have the correct form to constrain the dynamical variables, thereby eliminating the…

We review some of the recent results which can be useful for better understanding of the problem of stability of vacuum and in general classical solutions in higher derivative quantum gravity. The fourth derivative terms in the purely…

We provide a new proof of a important theorem in the Lagrangian formalism about necessary and sufficient conditions for a second-order variational system of equations to follow from a first-order Lagrangian.