Manuscript X-C@3 · X-C-v3.tex · section · 2260f5f8

Yang–Feldman characterization and quantum order

Yang–Feldman characterization and quantum order · lines 831–848

X-C@3#eq:interacting-operators

Define the linear interacting field and formal Green operators by

ϕ_{q} (c) E_{q}^{R} E_{q}^{A} = ϕ (R_{q} c), = (1 + E_{m}^{R} L [q])^{- 1} E_{m}^{R} = E_{m}^{R} (1 + L [q] E_{m}^{R})^{- 1}, = (1 + E_{m}^{A} L [q])^{- 1} E_{m}^{A} = E_{m}^{A} (1 + L [q] E_{m}^{A})^{- 1} .

These are finite formal expansions at the declared order. No assertion about numerical inversion of the perturbed operator is needed.

Displayed formulas in this passage

X-C@3#eq:interacting-operators · line 835
$ϕ_{q} (c) E_{q}^{R} E_{q}^{A} = ϕ (R_{q} c), = (1 + E_{m}^{R} L [q])^{- 1} E_{m}^{R} = E_{m}^{R} (1 + L [q] E_{m}^{R})^{- 1}, = (1 + E_{m}^{A} L [q])^{- 1} E_{m}^{A} = E_{m}^{A} (1 + L [q] E_{m}^{A})^{- 1} .$