Related papers: Second-order Lagrangians admitting a first-order H…
We study higher--order variational derivatives of a generic second--order Lagrangian ${\cal L}={\cal L}(x,\phi,\partial\phi,\partial^2\phi)$ and in this context we discuss the Jacobi equation ensuing from the second variation of the action.…
The conformal equivalence of fourth-order gravity following from a non-linear Lagrangian L(R) to theories of other types is widely known, here we report on a new conformal equivalence of these theories to theories of the same type but with…
Several alternative formulations of the first order approach to unimodular gravity are presented. There is always a particular one such that it is {\em classically} equivalent to the second order formulation; this we call {\em educated}. It…
For slowly varying fields on the scale of the lightest mass the logarithm of the vacuum functional of a massive quantum field theory can be expanded in terms of local functionals satisfying a form of the Schrodinger equation, the principal…
The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…
This paper deals with the time evolution in the matter era of perturbations in Friedman-Lemaitre models with arbitrary density parameter $\Omega$, with either a zero cosmological constant, $\Lambda = 0$, or with a non-zero cosmological…
By using the supersymmetric version of the Faddeev-Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In this approach the Hubbard ${\hat X}$-operators are used as field variables. In…
We address the problem of the existence of a Lagrangian for a given system of linear PDEs with constant coefficients. As a subtask, this involves bringing the system into a pre-Lagrangian form, wherein the number of equations matches the…
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…
Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems,…
We review recent progress concerning the analysis of Lagrangians on immersions into $\mathbb{R}^d$ depending on the first and second fundamental forms and their covariant derivatives.
The structure of a diffeomorphism invariant Lagrangians for an extended object W embedded in a bulk space M is discussed by following a close analogy with the relativistic particle in electromagnetic field as a system that is…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…
Li\'enard-type equations are used for the description of various phenomena in physics and other fields of science. Here we find a new family of the Li\'enard-type equations which admits a non-standard autonomous Lagrangian. As a by-product…
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…
Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…
Variational Relativity is a framework developed by Souriau in the sixties to better formulate General Relativity and its classical limit\,: Classical Continuum Mechanics. It has been used, for instance, to formulate Hyperelasticity in…
Effective Lagrangians containing arbitrary interactions of massive vector fields are quantized within the Hamiltonian path integral formalism. It is proven that correct Hamiltonian quantization of these models yields the same result as…
This article focuses on three main contributions. Firstly, we provide an in-depth overview of the nonlocal Lagrangian formalism. Secondly, we introduce an extended version of the second Noether's theorem tailored for nonlocal Lagrangians.…
The Hamiltonian of the Relativistic Theory of Gravitation (RTG) with nonzero graviton mass is derived. Scalar field is taken as a matter source. The second class constraints are excluded and Dirac brackets are obtained. There are no first…