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arXiv 1005.2945hep-thmath-phmath.MP
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非局部理论初值问题的一种新表述

A New Formulation of the Initial Value Problem for Nonlocal Theories

Neil Barnaby

备注：
36 pages, 9 figures. Accepted for publication in Nuclear Physics B
发表信息：
Nucl.Phys.B845:1-29,2011
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摘要：

有许多理由认为，局部性在微观尺度上是被破坏的，例如，在基本运动方程中存在无穷级数的高阶导数。这种类型的非定域性导致改进的紫外行为，新颖的宇宙动力学，是弦论的一般预测。另一方面，从根本上讲，非局部模型充满了复杂性，包括不稳定性和建立初始值问题的复杂性。我们研究了一类有趣的非局部模型的初值问题的结构。我们提倡一种新的新的公式，其中柯西表面是“涂抹”的基础规模的非局部性，使通常的概念，初始数据在t=0被替换为“初始函数”定义在-M^{-1} \leq t \leq 0，其中M是基础规模的非局部性。集中在一些具体的例子，从弦论和宇宙学，我们表明，这种数学重新制定了令人惊讶的影响，众所周知的稳定性问题。对于D-膜衰变在一个线性介子的背景下，我们能够表明，不稳定的方向相空间不能访问从一个物理上合理的初始函数。因此，在这个模型中不稳定解的先前例子对应于非物理的初始条件，在初始值问题的旧公式中被混淆的观察。我们还讨论了这种方法的非局部宇宙学模型的含义。

英文摘要：

There are a number of reasons to entertain the possibility that locality is violated on microscopic scales, for example through the presence of an infinite series of higher derivatives in the fundamental equations of motion. This type of nonlocality leads to improved UV behaviour, novel cosmological dynamics and is a generic prediction of string theory. On the other hand, fundamentally nonlocal models are fraught with complications, including instabilities and complications in setting up the initial value problem. We study the structure of the initial value problem in an interesting class of nonlocal models. We advocate a novel new formulation wherein the Cauchy surface is "smeared out" over the underlying scale of nonlocality, so that the the usual notion of initial data at t=0 is replaced with an "initial function" defined over -M^{-1} \leq t \leq 0 where M is the underlying scale of nonlocality. Focusing on some specific examples from string theory and cosmology, we show that this mathematical re-formulation has surprising implications for the well-known stability problem. For D-brane decay in a linear dilaton background, we are able to show that the unstable directions in phase space cannot be accessed starting from a physically sensible initial function. Previous examples of unstable solutions in this model therefore correspond to unphysical initial conditions, an observation which is obfuscated in the old formulation of the initial value problem. We also discuss implication of this approach for nonlocal cosmological models.

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