Volume-forms and Minimal Action Principles in Affine Manifolds

Through the analyses of volume-forms in differentiable manifolds, it is shown that the usual way of defining minimal action principles for field theory on curved space-times is not appropriate on non-riemannian manifolds. An alternative approach, based in a new volume-form, is proposed and confronted with the standard one. The new volume element is explicitly used in the study of Einstein-Cartan theory of gravity and its relation to string theory, in connection with some recent results on the subject.