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

Second moments and commutators

Finite families: spectral laws versus ordered Weyl correlations › Second moments and commutators · lines 852–866

For a residual state $ρ$ , define its field cross moments by

M_{ij}^{ρ} = ℓ \sum p_{ℓ} ⟨ Φ (v_{i}) ψ_{ℓ}, Φ (v_{j}) ψ_{ℓ} ⟩, b_{i}^{ρ} = ⟨ Φ (v_{i}) ⟩_{ρ} .

These sums exist by (eq:state-number). Set

C_{ij}^{ρ} = Re M_{ij}^{ρ} - b_{i}^{ρ} b_{j}^{ρ} .

Displayed formulas in this passage

unlabeled · line 855
$M_{ij}^{ρ} = ℓ \sum p_{ℓ} ⟨ Φ (v_{i}) ψ_{ℓ}, Φ (v_{j}) ψ_{ℓ} ⟩, b_{i}^{ρ} = ⟨ Φ (v_{i}) ⟩_{ρ} .$
unlabeled · line 863
$C_{ij}^{ρ} = Re M_{ij}^{ρ} - b_{i}^{ρ} b_{j}^{ρ} .$