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

One-oscillator retarded coefficient

The one-oscillator mixed insertion › Mixed Wick product and retarded coefficient · lines 2672–2698

V@1#fig:mixed-blocks-locality

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metricscalarrepresented quantumdefect / unresolvedsupport / scope
h^(x)=Qe(x)+Πr(x),[Q,Π]=iI\widehat h(x)=Qe(x)+\Pi r(x),\quad [Q,\Pi]=iI
The plane is symplectic in this section.
Rg,f=Q⊗Φ(ve)+Π⊗Φ(vr)\mathcal R_{g,f}=Q\otimes\Phi(v_e)+\Pi\otimes\Phi(v_r)
ba(w+)ba(w_+)
pair annihilation
ba†(w−)ba^\dagger(w_-)
exchange
b†a(w−)b^\dagger a(w_-)
exchange
b†a†(w+)b^\dagger a^\dagger(w_+)
pair creation

w±=(ve±ivr)/2w_\pm=(v_e\pm iv_r)/\sqrt2. Finite-rank cross kernels. No dense graviton space.

The metric commutator is not generally causal-support restricted. This scalar insertion uses one metric factor, so no metric–metric contraction enters.

One-oscillator retarded coefficient. The scalar contraction calculation leaves one oscillator factor and one scalar factor, giving four mixed particle blocks. These are finite-rank cross kernels. The oscillator-valued metric is not a local relativistic metric field, although its commutator with the scalar insertion has the causal support required for this single calculation.

Nearby in this section