The $\mathcal{L}$-Calculus for Causal Variational Principles: An Exterior Differential Calculus on Non-Smooth Spaces

Abstract

A differential calculus for causal variational principles is developed, which generalizes the exterior calculus of differential forms and some of the associated differential topological structures to non-smooth spaces. Our calculus includes the exterior derivative, de Rham cohomology, glueing constructions (restrictions and extensions of differential forms, Mayer-Vietoris sequence), a Künneth formula and Poincar{é}'s lemma. Moreover, we prove versions of Stokes' theorem and the Gauß divergence theorem. The constructions and results are illustrated by several examples.

57 pages, LaTeX, 6 figures