Symbol chi
chi is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Published equation contexts
Why this formula appears here
The detector, not the mode decomposition, is the object this article works with, for a reason that matters later: a detector’s response is what an experiment can actually report, while “the Bogoliubov coefficients of the true vacuum” is not the kind of thing any apparatus reads off a dial. The response functional for a pointlike, linearly coupled two-level (Unruh-DeWitt) detector on worldline x() , parametrized by its own proper time , with energy gap and switching function controlling when the interaction is on, is
Read the representative guide
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (2)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 9 · Evolutionary Physics
No Particle Without a Cosigner
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
The detector, not the mode decomposition, is the object this article works with, for a reason that matters later: a detector’s response is what an experiment can actually report, while “the Bogoliubov coefficients of the true vacuum” is not the kind of thing any apparatus reads off a dial. The response functional for a pointlike, linearly coupled two-level (Unruh-DeWitt) detector on worldline x() , parametrized by its own proper time , with energy gap and switching function controlling when the interaction is on, is
Meanings in this article
Equation guide → · Article →Equation 46 · Evolutionary Physics
No Particle Without a Cosigner
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
The first term is the field state — the same vacuum, or the same thermal state, or in curved spacetime the same choice among the Boulware, Hartle-Hawking, and Unruh states, since none of those is fixed by the geometry alone. The second is the coupling type: a detector linearly coupled to the field itself and a detector coupled to the field’s proper-time derivative are different instruments on the same worldline, and their response spectra carry different powers of in the numerator even for identical trajectories — Moustos showed exactly this, that a detector’s early-time response depends on which bilinear of the field it couples to, even though, remarkably, its late-time asymptotic…