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… 
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