Manuscript VIII-B@3 · VIII-B-v3.tex · section · 3aa6baa1

Expectation selection and spectator invariance

Expectation selection and spectator invariance · lines 1571–1589

VIII-B@3#eq:source-domain, VIII-B@3#eq:sourced-deficit

Fix $κ \in R$ and define the admitted state domain

D_{src} = {ϱ \in D (H_{Γ}) : μ_{0} + κ I_{f} (ϱ) \in I},

with the declared classical restrictions when present. For a fixed interpolation flag $θ \in [0, 1]$ , put

μ_{θ} (ϱ) = μ_{0} + θ κ I_{f} (ϱ) .

The principal rule uses $θ = 1$ . The domain is convex, although it need not be nonempty for every choice of fixed source and coupling.

Displayed formulas in this passage

VIII-B@3#eq:source-domain · line 1574
$D_{src} = {ϱ \in D (H_{Γ}) : μ_{0} + κ I_{f} (ϱ) \in I},$
VIII-B@3#eq:sourced-deficit · line 1582
$μ_{θ} (ϱ) = μ_{0} + θ κ I_{f} (ϱ) .$