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Equation 21 · Part 5 · The Entry a Relabeling Cannot Write

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DΛ:=Hf−Λ†(Hc).D_\Lambda := H_f - \Lambda^\dagger(H_c).
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

That pullback is the object this article is built around: DΛ:=Hf−Λ†(Hc)D_\Lambda := H_f - \Lambda^\dagger(H_c). DΛD_\Lambda is Hermitian on Hf\mathcal H_f — a positive, unital map applied to a self-adjoint input stays self-adjoint — and it carries units of energy, since both terms do. Its state-dependent reading,

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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