Related papers: Second-order multisymplectic field theory: A varia…
We use Noether symmetry approach to find spherically symmetric static solutions of the non-minimally coupled electromagnetic fields to gravity. We construct the point-like Lagrangian under the spherical symmetry assumption. Then we…
In earlier works on Shape Dynamics (SD), a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was developed in order to implicitly construct SD's global Hamiltonian and eliminate…
The general form of N=2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets, with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in…
The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between…
We propose a category of bundles in order to perform Lagrangian reduction by stages in covariant Field Theory. This category plays an analogous role to Lagrange-Poincar\'e bundles in Lagrangian reduction by stages in Mechanics and includes…
Building upon the Noether charge formalism of Iyer and Wald, we derive a variational formula for spacetimes admitting a Killing vector field, for a generic energy-momentum distribution with compact support. Applying this general result to…
We introduce a variational setting for the action functional of an autonomous and indefinite Lagrangian on a finite dimensional manifold. Our basic assumption is the existence of an infinitesimal symmetry whose Noether charge is the sum of…
A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…
A new geometric framework is developed to describe non-conservative classical field theories, which is based on multisymplectic and contact geometries. Assuming certain additional conditions and using the forms that define this multicontact…
We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial…
Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…
In 2025, Bernardes, Erler and Firat proposed a novel, elegant expression for the symplectic form on phase space applicable to non-local theories. We show that this BEF symplectic structure can be derived directly from an…
Results on symplectic spinors and their higher spin versions, concerning representation theory and cohomology properties are presented. Exterior forms with values in the symplectic spinors are decomposed into irreducible modules including…
This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems.…
A recent paper arXiv:1312.4890 on multi-symplectic magnetohydrodynamics (MHD) using Clebsch variables in an Eulerian action principle with constraints is further extended. We relate a class of symplecticity conservation laws to a vorticity…
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…
We apply ideas from conformal field theory to study symplectic four-manifolds, by using modular functors to "linearise" Lefschetz fibrations. In Chern-Simons theory this leads to the study of parabolic vector bundles of conformal blocks.…
A general slice theorem for the action of a Fr\'echet Lie group on a Fr\'echet manifolds is established. The Nash-Moser theorem provides the fundamental tool to generalize the result of Palais to this infinite-dimensional setting. The…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its non-trivial reducible gauge symmetries and their algebra are defined in this very general setting by means of the inverse second Noether…