Observatorio de I+D+i UPM

Memorias de investigación
Conferencias:
Second-order Lagrangians admitting a first-order Hamiltonian formalism
Año:2019
Áreas de investigación
  • Matemáticas
Datos
Descripción
From the earlier seventies thanks to the works of Goldschmidt and Stenberg and P. L. García among others, jet bundles constitute the natural geometric setting to develop the Lagrangian and Hamiltonian formalisms in the calculus of variations on fibred manifolds, as well as to study the presymplectic structure attached to a variational problem. As is known, classical fields can be viewed as the sections of fibred manifolds and the Lagrangian formalism are then formulated in terms of jet manifolds. In this setting, we study a class of second?order Lagrangian densities admitting a first?order Hamiltonian formalism; namely, for each second-order Lagrangian density on an arbitrary fibred manifold p. the Poincaré?Cartan form of which is projectable, by using a new notion of regularity previously introduced, a first?order Hamiltonian formalism is developed for such a class of variational problems; (2) the existence of first?order equivalent Lagrangians is discussed from a local point of view as well as global; (3) this formalism is then applied to classical Hilbert-?Einstein Lagrangian and a generalization of the BF theory. The results suggest that the class of problems discussed here constitutes a natural variational setting for General Relativity.
Internacional
Si
ISSN o ISBN
0000000000000
Entidad relacionada
Centre de Recerca Matemàtica
Nacionalidad Entidad
ESPAÑA
Lugar del congreso
Barcelona
Esta actividad pertenece a memorias de investigación
Participantes
  • Autor: Maria Eugenia Rosado Maria (UPM)
Grupos de investigación, Departamentos, Centros e Institutos de I+D+i relacionados
  • Creador: Grupo de Investigación: Geometría y sus aplicaciones
  • Departamento: Matemática Aplicada
S2i 2022 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)