Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries
The Hamiltonian description of mechanical or field models defined by singular Lagrangians plays a central role in physics. A number of methods are known for this purpose, the most popular of them being the one developed by Dirac. Here, we discuss other approaches to this problem that rely on the dir...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/8/1430 |
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| author | Fernando Barbero Marc Basquens Valle Varo Eduardo J. S. Villaseñor |
| author_facet | Fernando Barbero Marc Basquens Valle Varo Eduardo J. S. Villaseñor |
| author_sort | Fernando Barbero |
| collection | DOAJ |
| description | The Hamiltonian description of mechanical or field models defined by singular Lagrangians plays a central role in physics. A number of methods are known for this purpose, the most popular of them being the one developed by Dirac. Here, we discuss other approaches to this problem that rely on the direct use of the equations of motion (and the tangency requirements characteristic of the Gotay, Nester and Hinds method), or are formulated in the tangent bundle of the configuration space. Owing to its interesting relation with general relativity we use a concrete example as a test bed: an extension of the Pontryagin and Husain–Kuchař actions to four dimensional manifolds with boundary. |
| first_indexed | 2024-03-10T08:20:34Z |
| format | Article |
| id | doaj.art-7e93a34170de40e3a58b3bd4fdc41aee |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T08:20:34Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7e93a34170de40e3a58b3bd4fdc41aee2023-11-22T10:01:22ZengMDPI AGSymmetry2073-89942021-08-01138143010.3390/sym13081430Three Roads to the Geometric Constraint Formulation of Gravitational Theories with BoundariesFernando Barbero0Marc Basquens1Valle Varo2Eduardo J. S. Villaseñor3Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, SpainDepartamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, SpainDepartamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, SpainGrupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán (UC3M), Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, SpainThe Hamiltonian description of mechanical or field models defined by singular Lagrangians plays a central role in physics. A number of methods are known for this purpose, the most popular of them being the one developed by Dirac. Here, we discuss other approaches to this problem that rely on the direct use of the equations of motion (and the tangency requirements characteristic of the Gotay, Nester and Hinds method), or are formulated in the tangent bundle of the configuration space. Owing to its interesting relation with general relativity we use a concrete example as a test bed: an extension of the Pontryagin and Husain–Kuchař actions to four dimensional manifolds with boundary.https://www.mdpi.com/2073-8994/13/8/1430geometric constraint algorithmhamiltonian field theoryHusain–Kuchař modelpontryaginthree-dimensional general relativityboundaries |
| spellingShingle | Fernando Barbero Marc Basquens Valle Varo Eduardo J. S. Villaseñor Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries Symmetry geometric constraint algorithm hamiltonian field theory Husain–Kuchař model pontryagin three-dimensional general relativity boundaries |
| title | Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries |
| title_full | Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries |
| title_fullStr | Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries |
| title_full_unstemmed | Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries |
| title_short | Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries |
| title_sort | three roads to the geometric constraint formulation of gravitational theories with boundaries |
| topic | geometric constraint algorithm hamiltonian field theory Husain–Kuchař model pontryagin three-dimensional general relativity boundaries |
| url | https://www.mdpi.com/2073-8994/13/8/1430 |
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