Towards Hamiltonian Formalism for String Field Theory and Nonlocality

TL;DR

This paper develops a Hamiltonian formalism for a toy model inspired by string field theory, addressing nonlocality and ensuring physical consistency by constraining states, thus advancing the understanding of nonlocal quantum theories.

Contribution

It introduces a Hamiltonian framework for a string-inspired toy model that reproduces path-integral correlation functions and manages nonlocality through physical-state constraints.

Findings

Physical-state constraints eliminate negative-norm states.

Zero-norm states decouple from physical states.

The formalism offers a new perspective on string field theory nonlocality.

Abstract

String field theories exhibit exponential suppression of interactions among the component fields at high energies due to infinite-derivative factors such as $e^{\ell^2 \Box / 2}$ in the vertices. This nonlocality has hindered the development of a consistent Hamiltonian formalism, leading some to question whether such a formalism is even viable. To address this challenge, we introduce a toy model inspired by string field theory and construct its Hamiltonian formalism by demanding that it reproduce all correlation functions derived from the path-integral formalism. Within this framework, we demonstrate for this toy model that physical-state constraints can be imposed to eliminate negative-norm states, while zero-norm states decouple from the physical state space. This approach provides a novel perspective on the nonlocality inherent in string field theories.