7,131 research outputs found
Generalized Galilean Algebras and Newtonian Gravity
The non-relativistic versions of the generalized Poincar\'{e} algebras and
generalized -Lorentz algebras are obtained. This non-relativistic algebras
are called, generalized Galilean algebras type I and type II and denoted by
and
respectively. Using a generalized In\"{o}n\"{u}--Wigner contraction procedure
we find that the generalized Galilean algebras type I can be obtained from the
generalized Galilean algebras type II. The -expansion procedure allows us to
find the algebra from the Newton--Hooke
algebra with central extension. The procedure developed in Ref. \cite{newton}
allow us to show that the non-relativistic limit of the five dimensional
Einstein--Chern--Simons gravity is given by a modified version of the Poisson
equation. The modification could be compatible with the effects of Dark Matter,
which leads us to think that Dark Matter can be interpreted as a
non-relativistic limit of Dark Energy.Comment: 16 pages, no figures in 755 (2016) 433-43
Symmetry reduction, integrability and reconstruction in k-symplectic field theory
We investigate the reduction process of a k-symplectic field theory whose
Lagrangian is invariant under a symmetry group. We give explicit coordinate
expressions of the resulting reduced partial differential equations, the
so-called Lagrange-Poincare field equations. We discuss two issues about
reconstructing a solution from a given solution of the reduced equations. The
first one is an interpretation of the integrability conditions, in terms of the
curvatures of some connections. The second includes the introduction of the
concept of a k-connection to provide a reconstruction method. We show that an
invariant Lagrangian, under suitable regularity conditions, defines a
`mechanical' k-connection.Comment: 37 page
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