Symmetry and feasibility of infinitesimal transformations

Abstract

We consider the ten-dimensional vector space Open image in new window whose elements are generators of infinitesimal transformations of the tendimensional manifold Open image in new window of all the local reference frames. We indicate by Open image in new window the convex closed cone which contains the generators of the physically feasible transformations and we assume that Open image in new window is stable under a group Open image in new window of linear mappings of Open image in new window onto itself. The convex closed cones which are stable under the restricted Lorentz group form a family parametrized by a quantityl which we interpret as a new physical constant, in the simplest case a fundamental lenght. We discuss all the linear mappings which leave the cone Open image in new window stable and we show that, under reasonable assumptions, the symmetry group Open image in new window contains a group isomorphic to the restricted de Sitter groupSO2,3+ and possibly also a parity operator and the dilatations of the space Open image in new window .