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

External witness and switching

The external-metric first retarded product › Switching and the external gauge defect · lines 2494–2527

V@1#fig:external-witness-switch

metricscalarrepresented quantumdefect / unresolvedsupport / scope

(a)Free-null label, nonzero correction

f=P\rho,\quad \phi(f)=0,\quad u_f=-\rho

q_{g,h,f}=-\mathsf Q_{gh}\rho

\langle\Omega,\phi(q_{g,h,f})a^\dagger(v)\Omega\rangle\neq 0

$g=1$ near $\operatorname{supp}\rho$ . Off-shell label before representation. Fixed contact retained.

(b)Switch dependence

\mathsf Q_{gh}\phi=gL_h\phi-(\partial_\mu g)\bar h^{\mu\nu}\partial_\nu\phi

$g=1$ near $\operatorname{supp} f$ does not remove every past-switching term. Compact-support continuity is not $g\to 1$ .

External witness and switching. A free-null insertion label $P ρ$ can have a nonzero first retarded coefficient because time ordering is formed before free-field representation. Separately, derivatives of the compact interaction switch contribute through the causal past; constancy near the final smearing does not generally eliminate them or establish an adiabatic limit.

Nearby in this section

section: Switching and the external gauge defect