Lagrangian-Hamiltonian unified formalism for field theory
arXiv:math-ph/0212002 · doi:10.1063/1.1628384
Abstract
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for PDE's.
LaTeX file, 23 pages. Minor changes have been made. References are updated
References in corpus (6)
- Geometry of multisymplectic Hamiltonian first-order field theories
- Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries
- Geometry of Hamiltonean n-vectors in Multisymplectic Field Theory
- Finite dimesional Hamiltonian formalism for gauge and field theories
- Skinner-Rusk approach to time-dependent mechanics
- Covariant Hamiltonian formalism for the calculus of variations with several variables
Cited by in corpus (25)
- Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
- The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories
- Skinner-Rusk Unified Formalism for Optimal Control Systems and Applications
- Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems
- Multisymplectic unified formalism for Einstein-Hilbert Gravity
- Unambiguous Formalism for Higher-Order Lagrangian Field Theories
- Unified formalism for non-autonomous mechanical systems
- Gunther's formalism (k-symplectic formalism) in classical field theory: Skinner-Rusk approach and the evolution operator
- Unified formalism for higher-order non-autonomous dynamical systems
- A new multisymplectic unified formalism for second-order classical field theories
- Unified Lagrangian-Hamiltonian formalism for contact systems
- Higher-order contact mechanics
- k-cosymplectic classical field theories: Tulczyjew, Skinner--Rusk and Lie-algebroid formulations
- Hamilton-Jacobi theory in multisymplectic classical field theories
- Unified formalism for Palatini gravity
- Higher-order Mechanics: Variational Principles and other topics
- Covariant Hamiltonian field theory. Path integral quantization
- Unified formalism for higher-order variational problems and its applications in optimal control
- Griffiths Variational Multisymplectic Formulation for Lovelock Gravity
- BV quantization of covariant (polysymplectic) Hamiltonian field theory
- Skinner-Rusk formalism for k-contact systems
- A Hamiltonian formalism for general variational problems, with applications to first order gravity with basis
- Geometrical structures of higher-order dynamical systems and field theories
- Routh Reduction of Palatini Gravity in Vacuum
- Multisymplectic Formalism for Cubic Horndeski Theories