On the multisymplectic formalism for first order field theories
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Publication:1311943
DOI10.1016/0926-2245(91)90013-YzbMath0782.58057OpenAlexW1991302355WikidataQ115362840 ScholiaQ115362840MaRDI QIDQ1311943
José F. Cariñena, Mike Crampin, Luis A. Ibort
Publication date: 21 January 1994
Published in: Differential Geometry and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0926-2245(91)90013-y
HamiltonianLagrangiangauge transformationjet bundlemultisymplectic structurefirst order field theorymultimomentum map
Quantization in field theory; cohomological methods (81T70) Applications of global analysis to the sciences (58Z05) Jets in global analysis (58A20) Quantum field theory; related classical field theories (81T99) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Geometric quantization in the presence of an electromagnetic field
- A symplectic framework for field theories
- A global version of the inverse problem of the calculus of variations
- The polysymplectic Hamiltonian formalism in field theory and calculus of variations. I: The local case
- The Hamilton-Cartan formalism in the calculus of variations
- A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics
- Affine bundles and integrable almost tangent structures
- Integrable almost cotangent structures and Legendrian bundles
- Noncanonical groups of transformations, anomalies, and cohomology
- An alternative approach to the Cartan form in Lagrangian field theories
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