An exterior differential calculus, based on Lagrangian-mollified weak derivatives and osculating vacua, is constructed for non-smooth causal variational principles, with cohomology, Stokes and Gauss theorems, and worked lattice and discrete examples.
Moving Frames: Difference and Differential-Difference Lagrangians
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the equivariant formulation of the conservation laws arising from Noether's theorem. The differential-difference theory is not merely an amalgam of the differential and difference theories, but has additional features that reflect the need for the group action to preserve the prolongation structure. Projectable moving frames are introduced; these cause the invariant derivative operator to commute with shifts in the discrete variables. Examples include a Toda-type equation and a method of lines semi-discretization of the nonlinear Schr\"odinger equation.
fields
math-ph 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
The $\mathcal{L}$-Calculus for Causal Variational Principles: An Exterior Differential Calculus on Non-Smooth Spaces
An exterior differential calculus, based on Lagrangian-mollified weak derivatives and osculating vacua, is constructed for non-smooth causal variational principles, with cohomology, Stokes and Gauss theorems, and worked lattice and discrete examples.