The use of test functions to help define quadratic Lagrangian on a causal set

Abstract

In some other papers, the Lagrangians in the causal sets included coefficients that were to be computed by integrating over Alexandrov set. In those other papers, this integral was explicitly evaluated, which resulted in rather sophisticated expressions. On the other hand, in this paper, instead of evaluating this integral, it was left in an integral form where the actual fields were replaced with test functions (thus avoiding nonlinearities). The test functions get absorbed into equations in a very natural way, so the resulting formulas look elegant.