Manuscript Em06-B@1 · Em06-B-v1.tex · definition · 61e38859

Definition: Residual and displaced states

The free scalar carrier and unbounded moments · lines 677–696

Em06-B@1#def:states, Em06-B@1#eq:rho-tilde, Em06-B@1#eq:O

Let $ρ_{ϵ}$ be positive trace-class operators with

Tr ρ_{ϵ} = 1, n_{ϵ} = Tr (ρ_{ϵ} N) < \infty.

For a declared $z \in S (R^{3}; C)$ , put

ρ_{ϵ} = D (z / ϵ) ρ_{ϵ} D (z / ϵ)^{*} .

For $v = v (f, h, χ)$ , the represented relational coefficient is

O_{ϵ} = ϵ Φ (v), o = 2 Re ⟨ v, z ⟩ .

Displayed formulas in this passage