A contact geometry framework for field theories with dissipation

DOI10.1016/j.aop.2020.168092zbMath1433.53042arXiv1905.07354OpenAlexW3100158520MaRDI QIDQ1987500

Xavier Gràcia, Xavier Rivas, Jordi Gaset, Narciso Román-Roy, Miguel C. Muñoz-Lecanda

Publication date: 15 April 2020

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.07354

zbMATH Keywords

contact structureBurgers' equationHamiltonian field theory\(k\)-symplectic structureDe Donder-Weyl theorysystem with dissipation

Mathematics Subject Classification ID

Differential forms in global analysis (58A10) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Contact manifolds (general theory) (53D10) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Symmetries and conservation laws in mechanics of particles and systems (70S10) PDEs on manifolds (35R01)

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Cites Work

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• On the \(k\)-symplectic, \(k\)-cosymplectic and multisymplectic formalisms of classical field theories
• Le théorème de réduction de Marsden-Weinstein en géométrie cosymplectique et de contact. (The Marsden-Weinstein reduction theorem in cosymplectic and contact geometry)
• Multisymplectic Lagrangian and Hamiltonian formalisms of classical field theories
• p-almost tangent structures
• On the multisymplectic formalism for first order field theories
• Contact manifolds and dissipation, classical and quantum
• Lagrangian approach to evolution equations: symmetries and conservation laws
• Contact Hamiltonian mechanics
• Introduction to Smooth Manifolds
• Günther’s formalism (k-symplectic formalism) in classical field theory: Skinner–Rusk approach and the evolution operator
• Symmetries and infinitesimal symmetries of singular differential equations
• k-symplectic structures
• Applications of Contact Geometry and Topology in Physics
• Contact Hamiltonian systems
• Cosymplectic and contact structures for time-dependent and dissipative Hamiltonian systems
• An Introduction to Contact Topology
• SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY
• Partial Differential Equations in Action