Probability Distribution for Vacuum Energy Flux Fluctuations in Two Spacetime Dimensions

TL;DR

This paper derives the probability distribution for vacuum energy flux fluctuations in two-dimensional conformal field theory, revealing distinct symmetric flux distributions and their relation to energy density, with potential applications in quantum field theory.

Contribution

It constructs the probability distribution for vacuum energy flux fluctuations in two dimensions, including joint distributions with energy density, using different averaging functions.

Findings

Flux distribution is symmetric, unlike energy density.

Distribution involves a modified Bessel function, distinct from Gamma distribution.

Energy flux distribution is more centrally concentrated than energy density.

Abstract

The probability distribution for vacuum fluctuations of the energy flux in two dimensions will be constructed, along with the joint distribution of energy flux and energy density. Our approach will be based on previous work on probability distributions for the energy density in two dimensional conformal field theory. In both cases, the relevant stress tensor component must be averaged in time, and the results are sensitive to the form of the averaging function. Here we present results for two classes of such functions, which include the Gaussian and Lorentzian functions. The distribution for the energy flux is symmetric, unlike that for the energy density. In both cases, the distribution may possess an integrable singularity. The functional form of the flux distribution function involves a modified Bessel function, and is distinct from the shifted Gamma form for the energy density. By considering the joint distribution of energy flux and energy density, we show that the distribution of energy flux tends to be more centrally concentrated than that of the energy density. We also determine the distribution of energy fluxes, conditioned on the energy density being negative. Some applications of the results will be discussed.