← All parts of this equation

Equation 50 · Part 1 · No Particle Without a Cosigner

Symbol dotmathcal F_a

F˙a(Ω)  ∝  Ωe2πcΩ/a−1,Ω>0,\dot{\mathcal F}_a(\Omega) \;\propto\; \frac{\Omega}{e^{2\pi c \Omega / a} - 1}, \qquad \Omega > 0,
F˙a\dot{\mathcal F}_a

What this part means

dotmathcal FaF_a has a dot, marking the rate of change of the underlying indexed quantity with respect to the article’s time variable.

Its job in the formula

dotmathcal FaF_a has a dot, marking the rate of change of the underlying indexed quantity with respect to the article’s time variable.

The passage around this formula

The first check any new object owes the literature is that it reproduce the literature’s own answer in the case the literature has already solved. For a worldline held at constant proper acceleration a forever, coupled linearly to a massless scalar field in the ordinary vacuum, with the switching left on for all time, the Wightman function depends only on the proper-time separation and the standard Fourier transform is exact and textbook: the excitation-branch rate per unit proper time takes the Bose-Einstein form F˙a(Ω)  ∝  Ωe2πcΩ/a−1,Ω>0\dot{\mathcal F}_a(\Omega) \;\propto\; \frac{\Omega}{e^{2\pi c \Omega / a} - 1}, \qquad \Omega > 0. with the proportionality constant fixed by the detector’s coupling strength and dimension — irrelevant here, since it cancels the instant the spectrum is…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.