A Geometric Hamilton-Jacobi Theory for Classical Field Theories

zbMath1208.70028arXiv0801.1181MaRDI QIDQ5391229

David Martín de Diego, Manuel de León, Juan Carlos Marrero

Publication date: 6 April 2011

Full work available at URL: https://arxiv.org/abs/0801.1181

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Hamilton-Jacobi equations in mechanics (70H20) 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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On the role of geometry in statistical mechanics and thermodynamics. I. Geometric perspective ⋮ Geometric Hamilton–Jacobi theory for systems with external forces ⋮ A Hamilton–Jacobi formalism for higher order implicit Lagrangians ⋮ Hamilton-Jacobi theory for gauge field theories ⋮ Cosymplectic and contact structures for time-dependent and dissipative Hamiltonian systems ⋮ Hamilton-Jacobi theory in multisymplectic classical field theories ⋮ Geometric Hamilton–Jacobi theory on Nambu–Poisson manifolds ⋮ Hamilton-Jacobi diffieties ⋮ A Hamilton-Jacobi theory on Poisson manifolds ⋮ Cauchy data space and multisymplectic formulation of conformal classical field theories ⋮ A geometric Hamilton–Jacobi theory on a Nambu–Jacobi manifold ⋮ Existence of solutions for Hamiltonian field theories by the Hamilton–Jacobi technique ⋮ Reviewing the geometric Hamilton–Jacobi theory concerning Jacobi and Leibniz identities ⋮ Hamilton-Jacobi theory in Cauchy data space ⋮ Multicontact formulation for non-conservative field theories

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