ترغب بنشر مسار تعليمي؟ اضغط هنا

Generalized Bianchi identities in gauge-natural field theories and the curvature of variational principles

427   0   0.0 ( 0 )
 نشر من قبل Marcella Palese
 تاريخ النشر 2004
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

By resorting to Noethers Second Theorem, we relate the generalized Bianchi identities for Lagrangian field theories on gauge-natural bundles with the kernel of the associated gauge-natural Jacobi morphism. A suitable definition of the curvature of gauge-natural variational principles can be consequently formulated in terms of the Hamiltonian connection canonically associated with a generalized Lagrangian obtained by contracting field equations.



قيم البحث

اقرأ أيضاً

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} introd uction 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.
In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {em conserved Noether currents}. It turns out that along any section of the relevant gauge--natu ral bundle this density is the divergence of a skew--symmetric (tensor) density, which is called a {em superpotential} for the conserved currents. We describe gauge--natural superpotentials in the framework of finite order variational sequences according to Krupka. We refer to previous results of ours on {em variational Lie derivatives} concerning abstra
We consider the second variational derivative of a given gauge-natural invariant Lagrangian taken with respect to (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms. By requiring such a second variationa l derivative to vanish, {em via} the Second Noether Theorem we find that a covariant strongly conserved current is canonically associated with the deformed Lagrangian obtained by contracting Euler--Lagrange equations of the original Lagrangian with (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms lying in the kernel of the generalized gauge-natural Jacobi morphism.
218 - M. Palese , E. Winterroth 2011
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.
The purpose of this paper is to define the concept of multi-Dirac structures and to describe their role in the description of classical field theories. We begin by outlining a variational principle for field theories, referred to as the Hamilton-Pont ryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Secondly, we introduce multi-Dirac structures as a graded analog of standard Dirac structures, and we show that the graph of a multisymplectic form determines a multi-Dirac structure. We then discuss the role of multi-Dirac structures in field theory by showing that the implicit field equations obtained from the Hamilton-Pontryagin principle can be described intrinsically using multi-Dirac structures. Furthermore, we show that any multi-Dirac structure naturally gives rise to a multi-Poisson bracket. We treat the case of field theories with nonholonomic constraints, showing that the integrability of the constraints is equivalent to the integrability of the underlying multi-Dirac structure. We finish with a number of illustrative examples, including time-dependent mechanics, nonlinear scalar fields and the electromagnetic field.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا