More insights into symmetries in multisymplectic field theories
This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics and in the geometric formulation of these theories are clar...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/386339 |
| Online Access: | https://hdl.handle.net/2117/386339 https://dx.doi.org/10.3390/sym15020390 |
| Access Level: | Open access |
| Keyword: | Symplectic geometry Field theory (Physics) General relativity (Physics) Lagrangian and Hamiltonian field theories Jet bundles Multisymplectic forms Symmetries Noether symmetries Gauge symmetries Conserved quantities Multimomentum maps Geometria simplèctica Camps, Teoria dels (Física) Relativitat general (Física) 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 Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Summary: | This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics and in the geometric formulation of these theories are clarified. Finally, a general discussion is given on the structure of symmetries in the presence of constraints appearing in singular field theories. Symmetries of some typical theories in theoretical physics are analyzed through the construction of the relevant multimomentum maps which are the conserved quantities (by Noether’s theorem) on the (pre)multisymplectic phase spaces. |
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