%0 Journal Article
%T From quadratic Hamiltonians of polymomenta to abstract geometrical Maxwell-like and Einstein-like equations
%A Alexandru Oana
%A Mircea Neagu
%J Mathematics
%D 2012
%I arXiv
%X The aim of this paper is to create a large geometrical background on the dual 1-jet space J^{1*}(T,M) for a multi-time Hamiltonian approach of the electromagnetic and gravitational physical fields. Our geometric-physical construction is achieved starting only from a given quadratic Hamiltonian function of polymomenta H, which naturally produces a canonical nonlinear connection N, a canonical Cartan N-linear connection C\Gamma(N) and their corresponding local distinguished (d-) torsions and curvatures. In such a context, we construct some geometrical electromagnetic-like and gravitational-like field theories which are characterized by some natural geometrical Maxwell-like and Einstein-like equations. Some abstract and geometrical conservation laws for the multi-time Hamiltonian gravitational physical field are also given.
%U http://arxiv.org/abs/1202.4477v1