A general background of higher order geometry and induced objects on subspaces.
A geometrical analysis of the field equations in field theory.
A model of gauge theory with invariant variables.
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.
Chaos in D0 brane dynamics
We consider the classical and quantum dynamics of D0 branes within the Yang-Mills approximation. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. Chaotic dynamics in N=2 supersymmetric Yang-Mills theory is also discussed.
Connection space approach to ambiguities of gauge theories.
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.
Divergences in formal variational calculus and boundary terms in Hamiltonian formalism
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
Equivariance, variational principles, and the Feynman integral.
Erratum
Extended soliton solutions in an effective action for Yang-Mills theory.
Fields associated with autonomous dynamical systems. (Champs associés aux systèmes dynamiques autonomes.)
Gauge-independent Hamiltonian reduction of constrained systems.
Generalized symmetries of massless free fields on Minkowski space.
Hamiltonian approaches of field theory.