731 research outputs found
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
Lagrangian and we show that this quantity is conserved.Comment: 9 pages, slightly revised, to appear in Proc. Winter School "Geometry
and Physics", Srni (CZ) 200
Global Generalized Bianchi Identities for Invariant Variational Problems on Gauge-natural Bundles
We derive both {\em local} and {\em global} generalized {\em Bianchi
identities} for classical Lagrangian field theories on gauge-natural bundles.
We show that globally defined generalized Bianchi identities can be found
without the {\em a priori} introduction of a connection. The proof is based on
a {\em global} decomposition of the {\em variational Lie derivative} of the
generalized Euler--Lagrange morphism and the representation of the
corresponding generalized Jacobi morphism on gauge-natural bundles. In
particular, we show that {\em within} a gauge-natural invariant Lagrangian
variational principle, the gauge-natural lift of infinitesimal principal
automorphism {\em is not} intrinsically arbitrary. As a consequence the
existence of {\em canonical} global superpotentials for gauge-natural Noether
conserved currents is proved without resorting to additional structures.Comment: 24 pages, minor changes, misprints corrected, a misprint in the
coordinate expression of the Jacobi morphism corrected; final version to
appear in Arch. Math. (Brno
Lagrangian reductive structures on gauge-natural bundles
A reductive structure is associated here with Lagrangian canonically defined
conserved quantities on gauge-natural bundles. Parametrized transformations
defined by the gauge-natural lift of infinitesimal principal automorphisms
induce a variational sequence such that the generalized Jacobi morphism is
naturally self-adjoint. As a consequence, its kernel defines a reductive split
structure on the relevant underlying principal bundle.Comment: 11 pages, remarks and comments added, this version published in ROM
Infinitesimal Algebraic Skeletons for a (2 + 1)-dimensional Toda Type System
A tower for a (2+1)-dimensional Toda type system is constructed in terms of a series expansion of operators which can be interpreted as generalized Bessel coefficients; the result is formulated as an analog of the Baker-Campbell-Hausdorff formula. We tackle the problem of the construction of infinitesimal algebraic skeletons for such a tower and discuss some open problems arising along our approach
A variational perspective on classical Higgs fields in gauge-natural theories
Higgs fields on gauge-natural prolongations of principal bundles are defined
by invariant variational problems and related canonical conservation laws along
the kernel of a gauge-natural Jacobi morphism.Comment: 10 page
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