ABSTRACT
In this chapter, we find out how a local Lie transformation group acts on nonlocal objects such as discrete variables, finite-difference derivatives, lattice spacings, etc.
In contrast to differential operators, finite-difference operators are specified on a finite subset (a difference stencil) of the countable set of lattice points where the solution of the problem in question is to be sought. This nonlocality of operators (from the physical viewpoint, the presence of typical dimensional scales in the problem) results in specific properties of finite-difference operators, properties which are absent in the local differential model. In particular, we can mention right and left differentiations with the corresponding shifts, uniform and nonuniform lattices, and specific features of the difference Leibniz rule. As a result, there arises a specific calculus of infinitesimal transformations of difference variables.
