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 ξ2 that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in ξ2 reduces the action to a local two-derivative theory with a ξ2-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.
Highlights
The possible complications of nonlocality along time appear even at the classical level
We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory
Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in ξ2 reduces the action to a local twoderivative theory with a ξ2-dependent potential
Summary
The scalar field theory model we wish to study is motivated by bosonic open string field theory (OSFT) truncated to the tachyon field φ(x). Where we have the nonlocality parameter ξ2, defined to be the constant that multiplies ∂ ̃2 in the exponential This parameter controls the amount of delocalization of each field at the interaction. For most intents and purposes, we can forget about the constants multiplying L and delete all tildes, to find our final, simplest form of the nonlocal theory: Both the field φ and the derivatives are unit-free. If we are interested in a nonlocal theory of an (ordinary) massive scalar, we must change the +1 in the above kinetic term for −1 This is achieved by letting φ → −φ, ∂2 → −∂2, ξ2 → −ξ2, and changing the sign of the Lagrangian. Models sharing the same kinetic term as the p-adic string but involving more general interactions have been introduced to describe the
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