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The goal of this paper is to introduce one of the versions of theelectromagnetic Lagrangian on a causal set in such a way that would address thenon-locality issues inherent to causal set theory. The key idea is thatLagrangian density is assigned to the edges rather than points, and there is away of defining the concept of "neighboring edges" of a given edge in such away that each edge has only finitely many neighboring edges which wouldultimately allow for the theory to be local. That is to be contrasted withpoints where every point has infinitely many direct neighbors which is a sourceof non-locality. The edges are needed in order to define electromagneticLagrangian anyway, regardless of the consideration of locality; the novelty ofthis paper is to assign Lagrangian density to the edges as well. Also, in theother papers edges were both spacelike and timelike, while in this paper theyare only timelike. This makes calculations considerably more complicated, butit is crucial in preserving locality since the Lorentz group in a hyperplaneperpendicular to the edge is compact only if the edge is timelike.

Electromagnetic Lagrangian on a causal set that resides on edges rather than points