连续统QFT中Shannon互信息的几何
Geometry of the Shannon mutual information in continuum QFT
摘要：
我们分析了连续统中香农互信息的几何项和标度性质。这是做一个自由的无质量标量场理论在$d$维，在相干态减少相对于一个一般的微分流形。作为一个副产品，我们找到了一个表达式的减少概率密度找到一个特定的领域在一个球。我们还将引入并计算该概率携带的关于观测区域位置的Fisher信息。这是一个有趣的信息度量，它指的是物理空间中的点，尽管在相对论QFT中它们是标签，而不是波动的量子可观测量。
英文摘要：
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 QFT they are labels and not fluctuating quantum observables.
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