Euler-Poincare reduction for discrete field theories
Mathematical Physics
2008-11-26 v2 math.MP
Abstract
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed.
Cite
@article{arxiv.math-ph/0606033,
title = {Euler-Poincare reduction for discrete field theories},
author = {Joris Vankerschaver},
journal= {arXiv preprint arXiv:math-ph/0606033},
year = {2008}
}
Comments
24 pages, 3 figures (v2: simplified treatment)