Differential Calculus and Discrete Structures

TL;DR

This paper explores a deformation of differential calculus that transitions from continuous to discrete structures, providing a generalized framework beyond traditional lattice discretization for applications in physical theories.

Contribution

It introduces a generalized differential calculus framework on discrete sets, extending beyond standard lattice discretization methods.

Findings

Deformation connects continuum and discrete calculus.

Framework generalizes lattice discretization.

Relates to physical theories on discrete spaces.

Abstract

There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of differential calculus on discrete sets. This framework generalizes the usual (lattice) discretization.