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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($\tau$) , parametrized by its own proper time $\tau$ , with energy gap $\Omega$ and switching function $\chi(\tau)$ controlling when the interaction is on, is

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