Localization of nonlocal theories

TL;DR

This paper demonstrates that specific nonlocal scalar models inspired by string theory can be reformulated as local systems with an auxiliary variable, enabling well-defined quantization and solution classification.

Contribution

It introduces a local reformulation of nonlocal models using an auxiliary variable, providing new insights into their quantization and solution structure.

Findings

Equivalent local and nonlocal formulations established

Well-defined Cauchy problem and quantization demonstrated

Classification of exact nonperturbative solutions achieved

Abstract

We show that a certain class of nonlocal scalar models, with a kinetic operator inspired by string field theory, is equivalent to a system which is local in the coordinates but nonlocal in an auxiliary evolution variable. This system admits both Lagrangian and Hamiltonian formulations, and its Cauchy problem and quantization are well-defined. We classify exact nonperturbative solutions of the localized model which can be found via the diffusion equation governing the fields.