Manuscript V@1 · V.tex · figure · e7ddf37d

Locked sign conventions

Two questions and five distinct objects › Two sign corrections · lines 397–435

V@1#fig:sign-audit

metricscalarrepresented quantumdefect / unresolvedsupport / scope

(a)Identical response

L_h^+=-L_h

PS=L_h^+\phi=-L_h\phi

Both notations merge into the same Duhamel response and the same raw current.

additional current sign reversal

(b)Opposite causal orientations

classification

\mathsf E_r=\mathsf G_{r,A}-\mathsf G_{r,R}

scalar commutator

\Delta_m=G_R-G_A

The symbols stay distinct.

(c)Retarded sign chain

W_m^{\mathrm F}-W_m=iG_R

i(iG_R)=-G_R

\phi^{(1)}_{g,h}=-G_R\mathsf Q_{gh}\phi

u_f=-G_Af,\quad q_{g,h,f}=+\mathsf Q_{gh}u_f

The TT minus in $-\partial_i(gh^{ij}\partial_j u_f)$ belongs to $\mathsf Q$ , not to an extra convention.

Locked sign conventions. The two displayed notations for the fixed-time response are identical. Classification uses advanced-minus-retarded propagation, whereas the scalar commutator uses retarded-minus-advanced propagation. In the retarded coefficient, the sign of $- G_{R}$ is already absorbed when $u_{f} = - G_{A} f$ , giving $q_{g, h, f} = Q_{g h} u_{f}$ .

Nearby in this section

section: Two sign corrections