Ending index or upper bound: infty

The passage around this formula

defined whenever the denominator is finite and nonzero. Given two such normalized spectra, for a detector on worldline x and a detector on worldline y , define their disagreement as the total variation distance between the two probability densities: $D_{\rm det}(x,y) = \frac12 \int_0^\infty d\Omega\, \big| p_x(\Omega) - p_y(\Omega) \big|$. This is the object this article is actually about, so its bookkeeping has to be stated in full before any number is produced. $D_{\rm det}$ is a map from pairs of “treaty configurations” — worldline, field state, coupling type, and the gap/switching pair used to build the spectrum — to the real interval [0,1] ; it carries no physical units, because it is built entirely from normalized probability densities over $\Omega$ , whose…

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