Related papers: On a class of polynomial Lagrangians
We introduce a new method to construct a large family of Lagrangian surfaces in complex Euclidean plane by means of two planar curves making use of their usual product as complex functions and integrating the Hermitian product of their…
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
Special relativity beyond its basic treatment can be inaccessible, in particular because introductory physics courses typically view special relativity as decontextualized from the rest of physics. We seek to place special relativity back…
We shall use the variational decomposition technique in order to calculate equations of motion and Noether energy-momentum complex for some classes of non-linear gravitational Lagrangians within the first-order (Palatini) formalism. In…
The aim of the paper is to study some dynamic aspects coming from a tangent form, i.e. a time dependent differential form on a tangent bundle. The action on curves of a tangent form is natural associated with that of a second order…
We consider Lagrangians in Hamilton's principle defined on the tangent space $TG$ of a Lie group $G$. Invariance of such a Lagrangian under the action of $G$ leads to the symmetry-reduced Euler-Lagrange equations called the Euler-Poincar\'e…
In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincar\'e algebra. We first give some general properties of Lie superalgebras with some emphasis on the supersymmetric extension of the…
A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian…
This work contains an exposition of foundations of the variational calculus in fibered manifolds. The emphasis is laid on the geometric aspects of the theory. Especially functionals defined by real functions (Lagrange functions) or…
We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and…
The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a…
We carry out some algebraic and analytic properties of a new class of orthogonal polyanalytic polynomials, including their operational formulas, recurrence relations, generating functions, integral representations and different…
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…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted algebroids. We present the corresponding Tulczyjew triple for…
This article is devoted to finding classical point-particle equivalents for the fermion sector of the nonminimal Standard-Model Extension (SME). For a series of nonminimal operators, such Lagrangians are derived at first order in Lorentz…
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all…
Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard Lagrangians. This work shows that the procedure of deriving…
We construct new special Lagrangian submanifolds in complex Euclidean space using a pair of minimal Legendrian submanifolds in odd-dimensional spheres and certain Lagrangian surface belonging to a family that can be considered as a…
A second-order generalization of the fundamental Lepage form of geometric calculus of variations over fibered manifolds with 2-dimensional base is described by means of insisting on (i) equivalence relation "Lepage differential 2-form is…