A general background of higher order geometry and induced objects on subspaces.
A geometrical analysis of the field equations in field theory.
A new geometric setting for classical field theories
A new geometrical setting for classical field theories is introduced. This description is strongly inspired by the one due to Skinner and Rusk for singular lagrangian systems. For a singular field theory a constraint algorithm is developed that gives a final constraint submanifold where a well-defined dynamics exists. The main advantage of this algorithm is that the second order condition is automatically included.
A new Lagrangian dynamic reduction in field theory
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.
About boundary terms in higher order theories
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particular...
Canonical nonlinear connections in the multi-time Hamilton geometry.
Conservation laws for non-global Lagrangians.
Controllability of 3D low Reynolds number swimmers
In this article, we consider a swimmer (i.e. a self-deformable body) immersed in a fluid, the flow of which is governed by the stationary Stokes equations. This model is relevant for studying the locomotion of microorganisms or micro robots for which the inertia effects can be neglected. Our first main contribution is to prove that any such microswimmer has the ability to track, by performing a sequence of shape changes, any given trajectory in the fluid. We show that, in addition, this can be done...
Distinguished Riemann-Hamilton geometry in the polymomentum electrodynamics
In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics.
Equivariance, variational principles, and the Feynman integral.
Gauge-independent Hamiltonian reduction of constrained systems.
Hamiltonian approaches of field theory.
Lagrangian and hamiltonian aspects of Josephson type media
Multivector fields and connections. Applications to field theories.
Se estudia la integrabilidad de campos multivectoriales en variedades diferenciables y la relación entre algunos tipos de campos multivectoriales en un fibrado de jets y conexiones en dicho fibrado. Como caso particular se relacionan los campos multivectoriales integrables y las conexiones cuyas secciones integrales son holonómicas. Como aplicación de todo ello, estos resultados permiten escribir las ecuaciones de campo de las teorías clásicas de campos de primer orden en varias formas equivalentes....
On a Differential Equation with Left and Right Fractional Derivatives
Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05We treat the fractional order differential equation that contains the left and right Riemann-Liouville fractional derivatives. Such equations arise as the Euler-Lagrange equation in variational principles with fractional derivatives. We reduce the problem to a Fredholm integral equation and construct a solution in the space of continuous functions. Two competing approaches in formulating differential equations of fractional order...
On higher order geometry on anchored vector bundles
Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.
Quantum information from graviton-matter gas.
Schwinger-Fronsdal theory of abelian tensor gauge fields.
Some aspects of the homogeneous formalism in field theory and gauge invariance
We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended configuration bundle. This new approach can be interpreted as a suitable generalization to Field Theory of the homogeneous formalism for Hamiltonian Mechanics. As an example of application, we obtain the expression of a formal energy for a parametrized version of the Hilbert–Einstein...
Symmetries in finite order variational sequences
We refer to Krupka’s variational sequence, i.e. the quotient of the de Rham sequence on a finite order jet space with respect to a ‘variationally trivial’ subsequence. Among the morphisms of the variational sequence there are the Euler-Lagrange operator and the Helmholtz operator. In this note we show that the Lie derivative operator passes to the quotient in the variational sequence. Then we define the variational Lie derivative as an operator on the sheaves of the variational sequence. Explicit...