Manuscript Em06-A@1 · Em06-A-v1.tex · proposition · ee9923c6

Proposition: Fixed-CCR coherent displacement does not suffice

Repairs to the proof architecture and final release › Three errors excluded by the construction · lines 1321–1336 · proof included or linked

Em06-A@1#prop:fixedCCR

Let $v_{f} \neq = 0$ . In the unscaled representation, every coherent state $D (z) Ω$ has

Var_{D (z) Ω} (Φ (v_{f})) = ∥ v_{f} ∥^{2} > 0.

Thus coherent displacement alone, at fixed CCR and for the unscaled observable, does not prove the absolute vanishing-variance acceptance condition.

Proof. Apply (eq:displacement). Displacement changes the mean by a constant and leaves the centered vacuum variance unchanged.

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