Covariant Poisson brackets in geometric field theory

DOI10.1007/s00220-005-1287-8zbMath1074.53071arXivmath-ph/0408008OpenAlexW1971951217MaRDI QIDQ1781844

Sandro Vieira Romero, Michael Forger

Publication date: 8 June 2005

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0408008

zbMATH Keywords

covariant functional formalismmultisymplectic formalism

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Poisson manifolds; Poisson groupoids and algebroids (53D17) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05)

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Cites Work

• A Poisson bracket on multisymplectic phase space
• A symplectic framework for field theories
• A canonical structure for classical field theories
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• On the multisymplectic formalism for first order field theories
• On field theoretic generalizations of a Poisson algebra
• The Hamilton-Cartan formalism in the calculus of variations
• Geodesic fields in the calculus of variation for multiple integrals
• Invariant Commutators for the Quantized Gravitational Field
• Hamiltonian multivector fields and Poisson forms in multisymplectic field theory
• Symplectic geometry of the convariant phase space
• The Action Principle and Partial Differential Equations. (AM-146)
• THE POISSON BRACKET FOR POISSON FORMS IN MULTISYMPLECTIC FIELD THEORY
• The commutation laws of relativistic field theory
• General Relativity
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