← Mathematical compendium

Published equation contexts

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|

Why this formula appears here

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 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 Ω\Omega , whose…

Read the full article-specific guide →

Read the representative guide

DdetD_{\rm det}

Symbol D_rm det

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].

Read this term in its guide →
00

Starting index or lower bound: 0

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Read this term in its guide →
∞\infty

Ending index or upper bound: infty

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Read this term in its guide →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Learn the mathematics behind it

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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|.

Equation 24 · Evolutionary Physics

No Particle Without a Cosigner

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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 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 Ω\Omega , whose…

Meanings in this article

  • DdetD_{\rm det}: 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].
Equation guide → · Article →