Volume-forms and Minimal Action Principles in Affine Manifolds

TL;DR

This paper investigates the limitations of traditional minimal action principles on non-Riemannian manifolds and proposes a new volume-form approach, demonstrating its application in Einstein-Cartan gravity and string theory contexts.

Contribution

It introduces a novel volume-form for variational principles on affine manifolds, challenging the standard methods used in curved space-time field theories.

Findings

The new volume-form improves the formulation of action principles on affine manifolds.

Application to Einstein-Cartan theory reveals new insights into gravity models.

Connections to string theory are explored using the proposed volume-form.

Abstract

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.