On the elimination of the Lagrangian from the classical Galilean model

Comments: 11 pages, 5 figures

The classical Galilean model contains a large set of covariant Lagrangians and some of them are degenerate and are the ones that satisfy the standard equivalence relation. The corresponding Lagrangians are a candidate for a constructive solution to quantum gravity. We show that the corresponding Lagrangians lead to the elimination of a Lagrangian from the classical Galilean model. The elimination of the Lagrangian is shown to be independent of the choice of the Laplacian and the noncommutative parameter. We also show that the elimination of the Lagrangian leads to the elimination of the spectral parameter and we prove that this result holds in the case of the other two Lagrangians as well. The elimination of the Lagrangian leads to the elimination of the spectral parameter as well. Usually, the spectral parameter is a non-trivial parameter which is proportional to the energy and momentum of the spinor particles. We show that the spectral parameter can be taken as a fixed point. We also show that the reduction of the spectral parameter to zero, i.e., to zero energy, results in the elimination of the spectral parameter.