Probability distributions for quantum stress tensors in two and four dimensions

Chris Fewster, L. H. Ford, Thomas A. Roman

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The probability distributions for the smeared energy densities of quantum fields, in the two and four-dimensional Minkowski vacuum are discussed. These distributions share the property that there is a lower bound at a finite negative value, but no upper bound. Thus arbitrarily large positive energy density fluctuations are possible. In two dimensions we are able to give an exact unique analytic form for the distribution. However, in four dimensions, we are not able to give closed form expressions for the probability distribution, but rather use calculations of a finite number of moments to estimate the lower bound, and the asymptotic form of the tail of the distribution. The first 65 moments are used for these purposes. All of our four-dimensional results are subject to the caveat that these distributions are not uniquely determined by the moments. One can apply the asymptotic form of the electromagnetic energy density distribution to estimate the nucleation rates of black holes and of Boltzmann brains.
Original languageEnglish
Title of host publicationRelativity and Gravitation
Subtitle of host publication100 years after Einstein in Prague
EditorsJiří Bičák, Tomáš Ledvinka
Number of pages8
ISBN (Print)9783319067612
Publication statusPublished - 2014

Publication series

NameSpringer Proceedings in Physics

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