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 $p^{\frac{1}{2}{\partial }_t^2}$ 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.

19 pages, 3 figures

References in corpus (5)

• Localization of nonlocal theories
• Inflation in (Super-)renormalizable Gravity
• Non-local Lagrangian Mechanics: Noether theorem and Hamiltonian formalism
• Non-local Lagrangian fields: Noether's theorem and Hamiltonian formalism
• Non-local scalar fields in static spacetimes via heat kernels

Cited by in corpus (1)

• Foundations of ghost stability