Initial value problem in string-inspired nonlocal field theory

Abstract

We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory. The Lorentz-covariant action is characterized by a parameter ${\xi }^2$ that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in ${\xi }^2$ reduces the action to a local two-derivative theory with a ${\xi }^2$-dependent potential. This picture is supported by evidence that the redefinition maps the wildly oscillating rolling tachyon solutions of the nonlocal theory to conventional rolling in the new scalar potential. For general field configurations we exhibit an obstruction to a local Lorentz-covariant formulation, but we can still achieve a formulation local in time, as well as a light-cone formulation. These constructions provide an initial value formulation and a Hamiltonian. Their causality is consistent with a lack of superluminal behavior in the nonlocal theory.

49 pages, 14 figures

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• Topological defects in nonlocal field theories
• Symplectic structure in open string field theory I: Rolling tachyons
• Massive to Massless by Applying a Nonlocal Field Redefinition
• Fractional Particle and Sigma Model
• Evolutionary algorithms for multi-center solutions
• Classifying deviation from standard quantum behavior using Kullback Leibler divergence
• UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
• Towards Hamiltonian Formalism for String Field Theory and Nonlocality