The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories
arXiv:0905.4580 · doi:10.1016/j.geomphys.2010.02.003
Abstract
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.
29 pages, revised version as accepted for publication in J. Geom. Phys
References in corpus (1)
Cited by in corpus (27)
- Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems
- The Maxwell-Proca theory: definition and construction
- Unified formalism for higher-order non-autonomous dynamical systems
- Unified Lagrangian-Hamiltonian formalism for contact systems
- A new multisymplectic unified formalism for second-order classical field theories
- The Tulczyjew triple for classical fields
- Covariant canonical formulations of classical field theories
- Higher-order contact mechanics
- Hamilton-Jacobi Diffieties
- Tulczyjew Triples in Higher Derivative Field Theory
- Geometric Hamilton-Jacobi Field Theory
- Multisymplectic formalism and the covariant phase
- Bundle-theoretic methods for higher-order variational calculus
- Unified formalism for Palatini gravity
- Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of The Second Order Degenerate Lagrangians
- On Higher Derivatives as Constraints in Field Theory: a Geometric Perspective
- Variational Principles for multisymplectic second-order classical field theories
- Higher-order Mechanics: Variational Principles and other topics
- Regularity properties of fiber derivatives associated with higher-order mechanical systems
- Symplectic structures related with higher order variational problems
- Unified formalism for higher-order variational problems and its applications in optimal control
- Reductions of Topologically Massive Gravity II: First Order Realizations of Second Order Lagrangians
- A Hamiltonian formalism for general variational problems, with applications to first order gravity with basis
- Symplectic quantization of multi-field Generalized Proca electrodynamics
- Skinner-Rusk formalism for k-contact systems
- Geometrical structures of higher-order dynamical systems and field theories
- Multisymplectic Formalism for Cubic Horndeski Theories