Abstract
We extend previous work on quantum stress tensor operators which have been averaged over finite time intervals to include averaging over finite regions of space as well. The space and time averaging can be viewed as describing a measurement process for a stress tensor component, such as the energy density of a quantized field in its vacuum state. Although spatial averaging reduces the probability of large vacuum fluctuations compared to time averaging alone, we find that the probability distribution decreases more slowly than exponentially as the magnitude of the measured energy density increases. This implies that vacuum fluctuations can sometimes dominate over thermal fluctuations and potentially have observable effects.
Highlights
The vacuum state of a quantum field theory is an eigenstate of the Hamiltonian, the integral of the energy density over all space, it is not an eigenstate of the local energy density or of other components of the stress tensor
Two-dimensional conformal field theory (CFT) provides an interesting example, in which the relative effects of time and space averaging can be determined in detail
We found in the previous section that here the moments grow no faster than ðn=αÞ!, so this criterion is satisfied for α ≥ 1=2 and PðxÞ is uniquely determined by the moments
Summary
The vacuum state of a quantum field theory is an eigenstate of the Hamiltonian, the integral of the energy density over all space, it is not an eigenstate of the local energy density or of other components of the stress tensor. This implies the existence of vacuum fluctuations of the energy density and other quadratic operators. For these fluctuations to be finite, and physically meaningful, these operators must be averaged over a finite spacetime region. The spacetime average is meaningful and will have finite fluctuations described by a probability distribution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
