Canonical lifts in multisymplectic De Donder-Weyl Hamiltonian field theories
We define canonical lifts of vector fields to the multisymplectic multimomentum bundles of De Donder–Weyl Hamiltonian (first-order) field theories and to the appropriate premultisymplectic embedded constraint submanifolds on which singular field theories are studied. These new canonical lifts are us...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/417513 |
| Acceso en línea: | https://hdl.handle.net/2117/417513 https://dx.doi.org/10.1088/1751-8121/ad6654 |
| Access Level: | acceso abierto |
| Palabra clave: | De Donder-Weyl Hamiltonian field theories Covariant phase spaces Constraint analysis Canonical lifts Symmetries Noether Theorem Bundles of forms Multisymplectic forms Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories Classificació AMS::83 Relativity and gravitational theory::83C General relativity Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial |
| Sumario: | We define canonical lifts of vector fields to the multisymplectic multimomentum bundles of De Donder–Weyl Hamiltonian (first-order) field theories and to the appropriate premultisymplectic embedded constraint submanifolds on which singular field theories are studied. These new canonical lifts are used to study the so-called natural Noether symmetries present in both regular and singular Hamiltonian field theories along with their associated conserved quantities obtained from Noether’s theorem. The Klein–Gordon field, the Polyakov bosonic string, and Einstein–Cartan gravity in 3 + 1 dimensions are analyzed in depth as applications of these concepts; as a peripheral result obtained in the analysis of the bosonic string, we provide a new geometrical interpretation of the well-known Virasoro constraint. |
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