Symmetries in Classical Field Theory

Abstract

The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.

70S05; 70H33; 55R10; 58A20

References in corpus (12)

• Geometry of multisymplectic Hamiltonian first-order field theories
• De Donder-Weyl Equations and Multisymplectic Geometry
• Some geometric aspects of variational problems in fibred manifolds
• Covariant Hamiltonian field theory
• Singular Lagrangian Systems on Jet Bundles
• Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories
• Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries
• Geometry of Hamiltonean n-vectors in Multisymplectic Field Theory
• Geometric Structures in Field Theory
• On the Multimomentum Bundles and the Legendre Maps in Field Theories
• A general construction of Poisson brackets on exact multisymplectic manifolds
• A vertical exterior derivative in multisymplectic geometry and a graded Poisson bracket for nontrivial geometries

Cited by in corpus (28)

• Multisymplectic unified formalism for Einstein-Hilbert Gravity
• Extended Hamiltonian systems in multisymplectic field theories
• Geometric aspects of nonholonomic field theories
• Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory
• Curve Flows in Lagrange-Finsler Geometry, Bi-Hamiltonian Structures and Solitons
• Multicontact formulation for non-conservative field theories
• Reduction of polysymplectic manifolds
• Euler-Poincare reduction for discrete field theories
• A class of nonholonomic kinematic constraints in elasticity
• On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
• The momentum map for nonholonomic field theories with symmetry
• Hamilton-Jacobi theory in Cauchy data space
• Partial Differential Hamiltonian Systems
• Symmetries of second order differential equations on Lie algebroids
• Symmetry aspects of nonholonomic field theories
• Symmetries, Newtonoids vector fields and conservation laws in the Lagrangian $k$-symplectic formalism
• More insights into symmetries in multisymplectic field theories
• A review on geometric formulations for classical field theory: the Bonzom-Livine model for gravity
• Practical Introduction to Action-Dependent Field Theories
• Cauchy data space and multisymplectic formulation of conformal classical field theories
• Covariant momentum map for non-Abelian topological BF field theory
• Lagrangian field theories: ind/pro-approach and L-infinity algebra of local observables
• Coisotropic reduction in Multisymplectic Geometry
• Graded Poisson and Graded Dirac structures
• Nonholonomic constraints in $k$-symplectic Classical Field Theories
• Classical field theories from Hamiltonian constraint: Local symmetries and static gauge fields
• Geometry of Classical Nambu-Goldstone Fields
• Geometrical structures of higher-order dynamical systems and field theories