Manuscript VII-H@1 · VII-H.tex · section · d20d2a9f

Physical matching and the normalization ledger

Definition sheet for the quantum benchmark › Physical matching and the normalization ledger · lines 602–660

The following data are fixed throughout the benchmark.

Datum	Treatment
Free equation and field normalization	$□ φ = 0$ and the two-point function (eq:W); no mass or kinetic counterterm is compared
Preparation	The same Minkowski vacuum, not an arbitrary Hadamard state
Source and readout	The same calibrated $Q$ , $h$ , $f$ , and source sign
Ordering coordinates	Permitted only with the corresponding algebra and state transport
Coincident response normalization	A source-local contact convention, classified below
Regulator	Auxiliary; it must yield a limit satisfying the declared response axioms if it is used
Boundary conditions	None are varied; introducing a reflecting wall changes the model

A multiplicative change of $Q$ , a source rescaling, a new vacuum, or a mass shift is not a normalization convention in this comparison.

If a different normal-ordering representation writes $Q$ as a Wick square plus a smooth c-number, that c-number must be included so that the same calibrated operator and state are represented. It is not legitimate to keep the changed symbol and call the resulting preparation unchanged. The distinction between product data and a physical state is also explicit in XII-A CheungXIIA.

The source-local contact freedom concerns the convention for coincident differentiated composite insertions. Formally, an addition

\frac{ℏ c}{2} \int j (y)^{2} d^{4} y

to a connected source-functional normalization has mixed second derivative $ℏ c \int f h$ . It does not change the free field equation or the zero-source composite.

If an apparatus calibration also fixes this coincident response, then $c$ is fixed and the admissible class becomes smaller. The invariant experiment constructed below remains valid in that smaller class. No equivalence of unmatched overlapping source/readout calibrations is claimed.

Displayed formulas in this passage

unlabeled · line 647
$\frac{ℏ c}{2} \int j (y)^{2} d^{4} y$