Manuscript X-E-ST@1 · X-E-ST.tex · definition · 44614221

Definition: One tree, counted once

E4: the isolated matter-induced tree › Definition and normalization · lines 1391–1408

X-E-ST@1#def:tree, X-E-ST@1#eq:tau, X-E-ST@1#eq:one

Let

τ = : A_{1} [k_{1} [ϕ]] :, T_{mat} = κ^{2} τ .

Total Wick ordering includes all three scalar letters. The one-tree observable is

Φ_{one} = ϕ (f) + κ A_{1} [h + r] + κ^{2} (Q [h + r, h + r] + A_{1} [k] + τ) .

Displayed formulas in this passage

X-E-ST@1#eq:tau · line 1394
$τ = : A_{1} [k_{1} [ϕ]] :, T_{mat} = κ^{2} τ .$
X-E-ST@1#eq:one · line 1401
$Φ_{one} = ϕ (f) + κ A_{1} [h + r] + κ^{2} (Q [h + r, h + r] + A_{1} [k] + τ) .$