Geometry of the Shannon mutual information in continuum QFT

Understand

We analyze geometric terms and scaling properties of the Shannon mutual information in the continuum.

• This is done for a free massless scalar field theory in $d$-dimensions, in a coherent state reduced with respect to a general differentiable manifold.
• As a by-product, we find an expression for the reduced probability density of finding a certain field on a ball.
• We will also introduce and compute the Fisher information that this probability carries about the location of the observation region.