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Manuscript Em03-C@1 · Em03-C-v1.tex · figure · 47dd71ec

Covariance orientation

C0: the complete two-packet semiclassical baseline › Inherited state and the covariance convention · lines 371–387

Em03-C@1#fig:covariance

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Conjugate-linear test
a(h)=∫h‾ aout dωa(h)=\int \overline h\, a_{\mathrm{out}}\,d\omega
[bi,bj†]=δij[b_i,b_j^\dagger]=\delta_{ij}
bi=a(hi)b_i=a(h_i)
Aij=⟨bj†bi⟩A_{ij}=\langle b_j^\dagger b_i\rangle
⟨bi†bj⟩=Aji\langle b_i^\dagger b_j\rangle=A_{ji}
Used by tr⁡ρD(z)\operatorname{tr}\rho D(z), Γ(W)\Gamma(W), and Wick
Synthetic control: A12=0.2+0.1iA_{12}=0.2+0.1i is not A21A_{21}. Equal diagonals do not license a transpose.

Covariance orientation. The diagram is a convention check, not a numerical diagonalization and not a physical calibration.

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