Abstract
The vacuum state—or any other state of finite energy—is not an eigenstate of any smeared (averaged) local quantum field. The outcomes (spectral values) of repeated measurements of that averaged local quantum field are therefore distributed according to a non-trivial probability distribution. In this paper, we study probability distributions for the smeared stress tensor in two-dimensional conformal quantum field theory. We first provide a new general method for this task based on the famous conformal welding problem in complex analysis. Secondly, we extend the known moment generating function method of Fewster, Ford and Roman. Our analysis provides new explicit probability distributions for the smeared stress tensor in the vacuum for various infinite classes of smearing functions. All of these turn out to be given in the end by a shifted Gamma distribution, pointing, perhaps, at a distinguished role of this distribution in the problem at hand.
Highlights
According to the standard postulates of Quantum Theory, if an observable A is measured repeatedly in a state |Ψ, the possible measurement outcomes λ of A will be distributed according to a probability distribution
In part 1, we develop a novel method for computing probability distribution for the chiral smeared stress tensor in conformal QFTs (CFTs)
Given a solution to this problem for the diffeomorphism ρt (u) generated by f (u), we show how to obtain from wt± a solution to the problem of finding the probability distribution for Θ( f ) in the vacuum
Summary
According to the standard postulates of Quantum Theory, if an observable (self-adjoint operator) A is measured repeatedly in a state |Ψ , the possible measurement outcomes (spectral values) λ of A will be distributed according to a probability distribution. Closed form analytical expressions seem to be available only in the last case so far.2 There it was shown [12] that Gaussian averages of the energy density in the vacuum state are distributed according to a shifted Gamma distribution, whose parameters are given explicitly in terms of the central charge c of the theory and the variance of the Gaussian concerned. While the method of [12] applies to general test functions, it involves the solution of a nonlinear differentio-integral flow equation as an intermediate step and the only solutions known until now are Gaussian in form There is another (partly formal) approach, due to Baumann [2], that gives the characteristic function of the CFT vacuum probability distribution for general sampling functions in terms of a functional calculus expression. We extend the ideas of [12] to thermal states
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
