Manuscript X-B-ii@1 · X-B-ii-v1.tex · lemma · f1377602

Lemma: Wick termination

C2: the one-contraction boundary › The check, re-derived · lines 584–597 · proof included or linked

X-B-ii@1#lem:wick

For the pair (A1)–(A2),

V ⋆ F_{c} = V F_{c} + ℏ ⟨ V^{'}, Δ_{+} c ⟩, F_{c} ⋆ V = V F_{c} + ℏ ⟨ V^{'}, Δ_{+}^{T} c ⟩ .

Proof. $F_{c}^{(1)} = c$ and $F_{c}^{(n)} = 0$ for $n \geq 2$ , so the Wick sum has only the terms $n = 0, 1$ . For the second formula, $⟨ c, Δ_{+} V^{'} ⟩ = ⟨ V^{'}, Δ_{+}^{T} c ⟩$ .

Displayed formulas in this passage

unlabeled · line 587
$V ⋆ F_{c} = V F_{c} + ℏ ⟨ V^{'}, Δ_{+} c ⟩, F_{c} ⋆ V = V F_{c} + ℏ ⟨ V^{'}, Δ_{+}^{T} c ⟩ .$

Nearby in this section

section: The check, re-derived
proposition: Proposition: The one-contraction identity
proposition: Proposition: Restricted causal factorization for the one pair
section: The check, re-derived