Probability distributions of smeared quantum stress tensors
Abstract
We obtain in closed form the probability distribution for individual measurements of the stressenergy tensor of twodimensional conformal field theory in the vacuum state, smeared in time against a Gaussian test function. The result is a shifted gamma distribution with the shift given by the previously known optimal quantum inequality bound. For small values of the central charge it is overwhelmingly likely that individual measurements of the sampled energy density in the vacuum give negative results. For the case of a single massless scalar field, the probability of finding a negative value is 84%. We also report on computations for fourdimensional massless scalar fields showing that the probability distribution of the smeared square field is also a shifted gamma distribution, but that the distribution of the energy density is not.
 Publication:

Physical Review D
 Pub Date:
 June 2010
 DOI:
 10.1103/PhysRevD.81.121901
 arXiv:
 arXiv:1004.0179
 Bibcode:
 2010PhRvD..81l1901F
 Keywords:

 11.25.Hf;
 03.70.+k;
 04.62.+v;
 05.40.a;
 Conformal field theory algebraic structures;
 Theory of quantized fields;
 Quantum field theory in curved spacetime;
 Fluctuation phenomena random processes noise and Brownian motion;
 Quantum Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 9 pages, 1 figure. Minor edits implemented