Related papers: Alternative Lagrangians obtained by scalar deforma…
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…
In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently…
In a space of 4-dimensions, I will examine constrained variational problems in which the Lagrangian, and constraint scalar density, are concomitants of a (pseudo-Riemannian) metric tensor and its first two derivatives. The Lagrange…
The present paper studies a method of finding Lagrangian transformations, in the form of particle paths, for all scalar conservation laws having a smooth flux. These are found using the notion of weak diffeomorphisms. More precisely, from…
We use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, first-order Lagrangian functionals and their associated Euler-Lagrange PDEs, subject to contact transformations. The first chapter contains an…
In this paper we consider an alternative approach to "un-reduction". This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions…
We show that if a Lagrangian is invariant under a transformation (with the invariance defined in the standard manner), then the equations of motion obtained from it maintain their form under the transformation. We also show that the…
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh…
Lagrange scalar densities which are concomitants of two scalar fields, a pseudo-Riemannian metric tensor, and their derivatives of arbitrary differential order are investigated in a space of four-dimensions. I construct the most general…
This paper is a continuation of [13], where new variational principles were introduced based on the concept of anti-selfdual (ASD) Lagrangians. We continue here the program of using these Lagrangians to provide variational formulations and…
We consider the lagrangian $L=F(R)$ in classical (=non-quantized) two-dimensional fourth-order gravity and give new relations to Einstein's theory with a non-minimally coupled scalar field. We distinguish between scale-invariant lagrangians…
In a four-dimensional space, I shall construct all of the conformally invariant scalar-tensor field theories, which are flat space compatible; i.e., well-defined and differentiable when evaluated for a flat metric tensor and constant scalar…
A new representation of Lagrangians of 4D nonlinear electrodynamics is considered. In this new formulation, in parallel with the standard Maxwell field strength F, an auxiliary bispinor (tensor) field V is introduced. The gauge field…
We develop a theory of non-linear cosmological perturbations at superhorizon scales for a scalar field with a Lagrangian of the form $P(X,\phi)$, where $X=-\partial^{\mu}\phi\partial_{\mu}\phi$ and $\phi$ is the scalar field. We employ the…
We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields…
We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schr\"odinger algebra, these equations…
Ostrogradsky instability generally appears in nondegenerate higher-order derivative theories and this issue can be resolved by removing any existing degeneracy present in such theories. We consider an action involving terms that are at most…
As an alternative to the covariant Ostrogradski method, we show that higher-derivative relativistic Lagrangian field theories can be reduced to second differential-order by writing them directly as covariant two-derivative theories…
The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are…
We derive the gravitational Lagrangian to all orders of curvature when the canonical constraint algebra is deformed by a phase space function as predicted by some studies into loop quantum cosmology. The deformation function seems to be…