Symmetries of dynamically equivalent theories
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| Format: | Artículo científico |
| Sprache: | en |
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Sociedade Brasileira de Física
2006
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| _version_ | 1866814297898745856 |
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| author | I. V. Tyutin |
| author_facet | I. V. Tyutin |
| contents | Symmetries of dynamically equivalent theories I. V. Tyutin D. M. Gitman Física, Astronomía y Matemáticas Symmetries Lagrangian actions Constrained systems A natural and very important development of constrained system theory is a detail study of the relationbetween the constraint structure in the Hamiltonian formulation with specific features of the theory in the Lagrangianformulation, especially the relation between the constraint structure with the symmetries of the Lagrangianaction. An important preliminary step in this direction is a strict demonstration, and this is the aim ofthe present article, that the symmetry structures of the Hamiltonian action and of the Lagrangian action are thesame. This proved, it is sufficient to consider the symmetry structure of the Hamiltonian action. The latter problemis, in some sense, simpler because the Hamiltonian action is a first-order action. At the same time, the studyof the symmetry of the Hamiltonian action naturally involves Hamiltonian constraints as basic objects. One cansee that the Lagrangian and Hamiltonian actions are dynamically equivalent. This is why, in the present article,we consider from the very beginning a more general problem: how the symmetry structures of dynamicallyequivalent actions are related. First, we present some necessary notions and relations concerning infinitesimalsymmetries in general, as well as a strict definition of dynamically equivalent actions. Finally, we demonstratethat there exists an isomorphism between classes of equivalent symmetries of dynamically equivalent actions. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46436205 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.1B Vol.36 |
| format | Artículo científico |
| id | redalyc_46436205 |
| language | en |
| publishDate | 2006 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | Symmetries of dynamically equivalent theories I. V. Tyutin Física, Astronomía y Matemáticas Symmetries Lagrangian actions Constrained systems Symmetries of dynamically equivalent theories I. V. Tyutin D. M. Gitman Física, Astronomía y Matemáticas Symmetries Lagrangian actions Constrained systems A natural and very important development of constrained system theory is a detail study of the relationbetween the constraint structure in the Hamiltonian formulation with specific features of the theory in the Lagrangianformulation, especially the relation between the constraint structure with the symmetries of the Lagrangianaction. An important preliminary step in this direction is a strict demonstration, and this is the aim ofthe present article, that the symmetry structures of the Hamiltonian action and of the Lagrangian action are thesame. This proved, it is sufficient to consider the symmetry structure of the Hamiltonian action. The latter problemis, in some sense, simpler because the Hamiltonian action is a first-order action. At the same time, the studyof the symmetry of the Hamiltonian action naturally involves Hamiltonian constraints as basic objects. One cansee that the Lagrangian and Hamiltonian actions are dynamically equivalent. This is why, in the present article,we consider from the very beginning a more general problem: how the symmetry structures of dynamicallyequivalent actions are related. First, we present some necessary notions and relations concerning infinitesimalsymmetries in general, as well as a strict definition of dynamically equivalent actions. Finally, we demonstratethat there exists an isomorphism between classes of equivalent symmetries of dynamically equivalent actions. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46436205 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.1B Vol.36 |
| title | Symmetries of dynamically equivalent theories |
| topic | Física, Astronomía y Matemáticas Symmetries Lagrangian actions Constrained systems |
| url | https://www.redalyc.org/articulo.oa?id=46436205 |