Infinite derivatives vs integral operators. The Moeller-Zwiebach puzzle

Abstract

We study the relationship between integral and infinite-derivative operators. In particular, we examine the operator p12∂t2 that appears in the theory of p-adic string fields, as well as the Moyal product that arises in non-commutative theories. We also attempt to clarify the apparent paradox presented by Moeller and Zwiebach, which highlights the discrepancy between them.