Related papers: Junction conditions in a general field theory
If a Lagrangian defining a variational problem has order $k$ then its Euler-Lagrange equations generically have order $2k$. This paper considers the case where the Euler-Lagrange equations have order strictly less than $2k$, and shows that…
We study problems of the calculus of variations and optimal control within the framework of time scales. Specifically, we obtain Euler-Lagrange type equations for both Lagrangians depending on higher order delta derivatives and…
We prove both necessary and sufficient second order conditions of extrema for variational problems involving any higher order continuously twice differentiable Lagrangians with multi-valued dependent functions of several variables. Our…
The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the…
In this work we propose a new and more general approach to the calculus of variations on time scales that allows to obtain, as particular cases, both delta and nabla results. More precisely, we pose the problem of minimizing or maximizing…
The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the…
We compute the Hamiltonian surface charges of gravity for a family of conservative boundary conditions, that include Dirichlet, Neumann, and York's mixed boundary conditions defined by holding fixed the conformal induced metric and the…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
We continue the study of symmetries in the Lagrangian formalism of arbitrary order with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second-order equations and arbitrary vector fields we are able to establish…
In general, the system of $2$nd-order partial differential equations made of the Euler-Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. The first aim of…
One of the fundamental problems of the theoretical physics is the search of the axioms, which ought to be the basis for the one-valued construction of Lagrangians of the relativistic fields. The creation of the gauge fields theory was the…
We consider a class of variational equations with exponential nonlinearities on a compact Riemannian surface, describing the mean field equation of the equilibrium turbulance with arbitrarily signed vortices. For the first time, we consider…
If a mathematical theory contains incompatible postulates then it is likely that the theory will produce theorems or results that are contradictory. It will be shown that this is the case with Dirac field theory. An example of such a…
In this paper we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical…
Galbrun's equation, which is a second order partial differential equation describing the evolution of a so-called Lagrangian displacement vector field, can be used to study acoustics in background flows as well as perturbations of…
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…
The fractional calculus of variations is now a subject under strong research. Different definitions for fractional derivatives and integrals are used, depending on the purpose under study. In this paper the fractional operators are defined…
Electromagnetism, the strong and the weak interaction are commonly formulated as gauge theories in a Lagrangian description. In this paper we present an alternative formal derivation of U(1)-gauge theory in a manifestly covariant Hamilton…
We study the Weak Gravity Conjecture in the presence of scalar fields. The Weak Gravity Conjecture is a consistency condition for a theory of quantum gravity asserting that for a U(1) gauge field, there is a particle charged under this…