# Covariant field theory on frame bundles of fibered manifolds

@article{McLean2000CovariantFT, title={Covariant field theory on frame bundles of fibered manifolds}, author={M. McLean and Larry K. Norris}, journal={Journal of Mathematical Physics}, year={2000}, volume={41}, pages={6808-6823} }

We show that covariant field theory for sections of π : E→M lifts in a natural way to the bundle of vertically adapted linear frames LπE. Our analysis is based on the fact that LπE is a principal fiber bundle over the bundle of 1-jets J1π. On LπE the canonical soldering 1-forms play the role of the contact structure of J1π. A lifted Lagrangian L: LπE→R is used to construct modified soldering 1-forms, which we refer to as the Cartan–Hamilton–Poincare 1-forms. These 1-forms on LπE pass to the…

## 38 Citations

n-symplectic Hamilton-Jacobi Theory

- 2005

In previous work n-symplectic geometry on the adapted frame bundle λ : LπE → E of an n = (m + k)-dimensional fiber bundle π : E → M has been used to forumulate covariant Lagrangian field theory that…

n-symplectic algebra of observables in covariant Lagrangian field theory

- Physics
- 2001

n-symplectic geometry on the adapted frame bundle λ:LπE→E of an n=(m+k)-dimensional fiber bundle π:E→M is used to set up an algebra of observables for covariant Lagrangian field theories. Using the…

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Abstract We construct momentum mappings for covariant Hamiltonian field theories using a generalization of symplectic geometry to the bundle L V Y of vertically adapted linear frames over the bundle…

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- 2015

By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian…

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- 2011

The objective of this work is twofold:
First, we analyze the relation between the
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In…

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- 2009

The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those…

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We investigate the reduction process of a $k$-symplectic field theory whose Lagrangian is invariant under a symmetry group. We give explicit coordinate expressions of the resulting reduced partial…

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For the bundle of linear frames LM of a manifold M, diffeomorphism invariance on the vertically adapted linear frame bundle L π (LM) and its infinitesimal counterpart, invariance under the natural…

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