Showing papers by "Libera! published in 1980"
23 citations
TL;DR: In this article, the authors consider the case in which all the constant solutions are generated by the action of a symmetry group on a given constant solution, where the spacej can be considered as the manifold of a Lie group.
Abstract: Given a system of matter and geometric fields defined on the ten-dimensional spacej of the local reference frames, we find the conditions which have to be satisfied by the Lagrangian if we require that the theory has a given set of constant solutions. The constant solutions describe empty regions, where the spacej can be considered as the manifold of a Lie group. We consider with more details the case in which all the constant solutions are generated by the action of a symmetry group on a given constant solution. We analyse a large class of symmetry groups and we find, as particular cases, some Lagrangians which have been proposed and studied recently. We find also some interesting theories symmetric with respect to a de SitterSO3,2 orSO4,1 group. They contain a microscopic fundamental length and have a nonlocal character.
10 citations
4 citations
TL;DR: In this article, it has been remarked that one should consider also tests of a more general kind, which are statistical mixtures of the pure tests mentioned above, as well as statistical mixture of pure tests.
Abstract: The general physical theories are often formulated in terms of observables (called (, tests ~) or (~ questions ~)(~.2) with two possible results, say 0 or 1. These tests are usually represented by sets in the phase space in classical mechanics and by projection operators in quantum theory. However, it has been remarked (3.a) that one should consider also tests of a more general kind, which are statistical mixtures of the pure tests mentioned above. In classical mechanics these tests are represented by a function ](P) in phase space with
1 citations