Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-05-17
Nucl.Phys.B845:1-29,2011
Physics
High Energy Physics
High Energy Physics - Theory
36 pages, 9 figures. Accepted for publication in Nuclear Physics B
Scientific paper
10.1016/j.nuclphysb.2010.11.016
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.
No associations
LandOfFree
A New Formulation of the Initial Value Problem for Nonlocal Theories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A New Formulation of the Initial Value Problem for Nonlocal Theories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A New Formulation of the Initial Value Problem for Nonlocal Theories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-299026