A Noether Theorem for discrete Covariant Mechanics

Noether's theorem is an elegant and powerful tool of classical mechanics, but it is of little to no consequence in discrete theories. Here we define and explore a discrete approach to covariant mechanics and show that within this framework a discrete version of Noether's theorem, completely analogous to the well-known continuum version with all its ramifications, remains valid. We also discuss why more traditional approaches to discretized mechanics violate certain conservation laws by construction.