arXiv subjects
Publications and source records attributed to L. O. Pimentel.
A nonlocal method to obtain discrete classical fields is presented. This technique relies on well-behaved matrix representations of the derivatives constructed on a non--equispaced lattice. The drawbacks of lattice theory like the fermion doubling or the breaking of chiral symmetry for the massless case, are absent in this method.
A useful finite-dimensional matrix representation of the derivative of periodic functions is obtained by using some elementary facts of trigonometric interpolation. This NxN matrix becomes a projection of the angular derivative into polynomial subspaces of finite dimension and it can be interpreted as a generator of discrete rotations associated to the z-component of the projection of the angular momentum operator in such subspaces, inheriting thus some properties of the continuum operator. The group associated to these discrete rotations is the cyclic group of order N. Since the square of the quantum angular momentum L^2 is associated to a partial differential boundary value problem in the angular variables $θ$ and $ϕ$ whose solution is given in terms of the spherical harmonics, we can project such a differential equation to obtain an eigenvalue matrix problem of finite dimension by extending to several variables a projection technique for solving numerically two point boundary value problems and using the matrix representation of the angular derivative found before. The eigenvalues of the matrix representing L^2 are found to have the exact form n(n+1), counting the degeneracy, and the eigenvectors are found to coincide exactly with the corresponding spherical harmonics evaluated at a certain set of points.
In the context of a family os scalar-tensor theories with a dynamical $Λ$, that is a binomial on the scalar field, the cosmological equations are considered. A general barotropic state equation $p=(γ-1)ρ$, for a perfect fluid is used for the matter content of the Universe. Some Friedmann- Robertson-Walker exact solutions are found, they have scale factor wich shows exponential or power law dependence on time. For some models the singularity can be avoided. Cosmological parameters as $Ω_m$, $Ω_Λ$, $q_0$ and $t_0$ are obtained and compared with observational data.