Related papers: A variational setting for an indefinite Lagrangian…
It is shown that given a Lagrangian for a system with a finite number of degrees of freedom, the existence of a variational symmetry is equivalent to the existence of coordinates in the extended configuration space such that one of the…
We consider static, cylindrically symmetric configurations in general relativity coupled to nonlinear electrodynamics (NED) with an arbitrary gauge-invariant Lagrangian of the form $L_{em}= \Phi(F)$, $F =F_{mn}F^{mn}$. We study electric and…
Infinitesimal variation of Action functional in classical (non-quantum) field theory with higher derivatives is presented in terms of well-defined intrinsic geometric objects independent of the particular field which varies. 'Integration by…
Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a…
This paper presents a formulation of Noether's theorem for fractional classical fields. We extend the variational formulations for fractional discrete systems to fractional field systems. By applying the variational principle to a…
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…
A frame independent formulation of analytical mechanics in the Newtonian space-time is presented The differential geometry of affine values i.e., the differential geometry in which affine bundles replace vector bundles and sections of one…
We construct, for a homogeneous Lagrangian of arbitrary order in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is null. This is similar to the property of the `fundamental…
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…
We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…
On the basis of the gauge principle of field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized…
We study Lagrangian systems with a finite number of degrees of freedom that are non-local in time. We obtain an extension of Noether theorem and Noether identities to this kind of Lagrangians. A Hamiltonian formalism is then set up for this…
Surprisingly, an interesting property of the Noether charge that it is by itself invariant under the corresponding symmetry transformation is never discussed in quantum field theory or classical mechanics textbooks we have checked. This…
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…
In this article, we analyze the Pontryagin model adopting different geometric-covariant approaches. In particular, we focus on the manner in which boundary conditions must be imposed on the background manifold in order to reproduce an…
In field theory, as well as in mechanics, the substitution of some fields in terms of other fields at the level of the action raises an issue of consistency with respect to the equations of motion. We discuss this issue and give an…
A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\epsilon$ to an arbitrary function of time, the Noether charge $Q$ is then the coefficient of $\dot\epsilon$ in the variation of the action.…
Any given system of ordinary differential equations in $n$-dimensional configuration space can be obtained from a peculiar variational problem with one local symmetry. The obtained action functional leads to the Hamiltonian formulation in…
We apply the converse of Noether's second theorem to the first-order $n$-dimensional Lovelock action, considering the frame rotation group as both $SO\left(1,n-1\right)$ or as $SO(n)$. As a result, we get the well-known invariance under…
We give a Lagrangian description of an electric charge in a field sourced by a continuous magnetic monopole distribution. The description is made possible thanks to a doubling of the configuration space. The Legendre transform of the…