89 research outputs found
On the Multimomentum Bundles and the Legendre Maps in Field Theories
We study the geometrical background of the Hamiltonian formalism of
first-order Classical Field Theories. In particular, different proposals of
multimomentum bundles existing in the usual literature (including their
canonical structures) are analyzed and compared. The corresponding Legendre
maps are introduced. As a consequence, the definition of regular and
almost-regular Lagrangian systems is reviewed and extended from different but
equivalent ways.Comment: LaTeX file, 19 pages. Replaced with the published version. Minor
mistakes are correcte
Geometry of Lagrangian First-order Classical Field Theories
We construct a lagrangian geometric formulation for first-order field
theories using the canonical structures of first-order jet bundles, which are
taken as the phase spaces of the systems in consideration. First of all, we
construct all the geometric structures associated with a first-order jet bundle
and, using them, we develop the lagrangian formalism, defining the canonical
forms associated with a lagrangian density and the density of lagrangian
energy, obtaining the {\sl Euler-Lagrange equations} in two equivalent ways: as
the result of a variational problem and developing the {\sl jet field
formalism} (which is a formulation more similar to the case of mechanical
systems). A statement and proof of Noether's theorem is also given, using the
latter formalism. Finally, some classical examples are briefly studied.Comment: Latex file, 48 page
A geometrical analysis of the field equations in field theory
In this review paper we give a geometrical formulation of the field equations
in the Lagrangian and Hamiltonian formalisms of classical field theories (of
first order) in terms of multivector fields. This formulation enables us to
discuss the existence and non-uniqueness of solutions, as well as their
integrability.Comment: 14 pages. LaTeX file. This is a review paper based on previous works
by the same author
Remarks on multisymplectic reduction
The problem of reduction of multisymplectic manifolds by the action of Lie
groups is stated and discussed, as a previous step to give a fully covariant
scheme of reduction for classical field theories with symmetries.Comment: 9 pages. Some comments added in the section "Discussion and outlook"
and in the Acknowledgments. New references are added. Minor mistakes are
correcte
Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries
We state the intrinsic form of the Hamiltonian equations of first-order
Classical Field theories in three equivalent geometrical ways: using
multivector fields, jet fields and connections. Thus, these equations are given
in a form similar to that in which the Hamiltonian equations of mechanics are
usually given. Then, using multivector fields, we study several aspects of
these equations, such as the existence and non-uniqueness of solutions, and the
integrability problem. In particular, these problems are analyzed for the case
of Hamiltonian systems defined in a submanifold of the multimomentum bundle.
Furthermore, the existence of first integrals of these Hamiltonian equations is
considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl
general symmetries} of the system is discussed. Noether's theorem is also
stated in this context, both the ``classical'' version and its generalization
to include higher-order Cartan-Noether symmetries. Finally, the equivalence
between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be
published in J. Phys. A: Mathematical and Genera
Symplectic Cuts and Projection Quantization
The recently proposed projection quantization, which is a method to quantize
particular subspaces of systems with known quantum theory, is shown to yield a
genuine quantization in several cases. This may be inferred from exact results
established within symplectic cutting.Comment: 12 pages, v2: additional examples and a new reference to related wor
A general construction of Poisson brackets on exact multisymplectic manifolds
In this note the long standing problem of the definition of a Poisson bracket
in the framework of a multisymplectic formulation of classical field theory is
solved. The new bracket operation can be applied to forms of arbitary degree.
Relevant examples are discussed and important properties are stated with proofs
sketched.Comment: 8 pages LaTeX, Talk delivered at the 34th Symp. on Math. Phys.,
Torun, Poland, June 200
Reconstrucción y adaptación de bastidor en la estructura de un cuadricielo para generar un "Tri-car"
The aim of this project is to put into practice all the knowledge acquired during the four years of study in the electromechanical automotive degree program at University of San Francisco. A thorough investigation of everything that falls within the area of construction, adaptation, restoration and assembly of systems, mechanisms and parts which takes a "Tri-car" was carried out. It has been analyzed to detail all the aspects involved in the creation of a frame that fits the tubular structure of a quad, which was put into practice and served for the optimal development of this project.El presente proyecto tiene como finalidad poner en práctica todos los conocimientos obtenidos en los cuatro años de estudio en la carrera de electromecánica automotriz en la Universidad San Francisco de Quito. Se efectuó una investigación minuciosa de todo lo que compete al área de construcción, adaptación, restauración y ensamblaje de los sistemas, mecanismos y piezas que lleva un “Tri-car”. Por lo cual se analizó detalladamente los aspectos concernientes a la generación de un bastidor adaptable a la estructura tubular de un cuadriciclo, lo cual se puso en práctica y fue utilizado para el desarrollo óptimo del proyecto
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