Geometry of the Shannon mutual information in continuum QFT

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 re...

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Bibliographic Details
Published in:Physical review. D 2017-06, Vol.95 (12), Article 125005
Main Authors: Junior, David R., Oxman, Luis E.
Format: Article
Language:English
Subjects:
Field theory
Fisher information
Quantum field theory
Quantum theory
Relativistic theory
Variation
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Summary: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. This is an interesting information measure that refers to points in physical space, although in relativistic quantum field theory they are labels and not fluctuating quantum observables.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.95.125005