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Equation 24 · Part 3 · No Particle Without a Cosigner

Symbol y

Ddet(x,y)=12∫0∞dΩ ∣px(Ω)−py(Ω)∣.D_{\rm det}(x,y) = \frac12 \int_0^\infty d\Omega\, \big| p_x(\Omega) - p_y(\Omega) \big|.
yy

What this part means

y is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

y is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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: Ddet(x,y)=12∫0∞dΩ ∣px(Ω)−py(Ω)∣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. DdetD_{\rm det} is a map from pairs of “treaty…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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