Manuscript X-F@1 · X-F.tex · definition · f35cc129

Definition: The three trees and the all-tree observable

F3: three trees › Definition · lines 946–964

X-F@1#def:trees, X-F@1#eq:trees, X-F@1#eq:all-tree

T_{mat} T_{mix} T_{self} := : A_{1} [Δ_{R}^{gr} (\frac{1}{2} g Θ)] :, := : A_{1} [Δ_{R}^{gr} (- σ_{ε} Q^{(1)} [h_{cl}] h)] :, := : A_{1} [Δ_{R}^{gr} (- \frac{1}{2} σ_{ε} G_{2} [h, h])] :,

so that $: A_{1} [k] := T_{mat} + T_{mix} + T_{self}$ . The all-tree observable is

Φ^{F} (f) = ϕ (f) + κ A_{1} [h] + κ^{2} (Q [h, h] + A_{1} [k_{cl}] + T_{mat} + T_{mix} + T_{self}), h = h_{cl} + h .

Displayed formulas in this passage

X-F@1#eq:trees · line 948
$T_{mat} T_{mix} T_{self} := : A_{1} [Δ_{R}^{gr} (\frac{1}{2} g Θ)] :, := : A_{1} [Δ_{R}^{gr} (- σ_{ε} Q^{(1)} [h_{cl}] h)] :, := : A_{1} [Δ_{R}^{gr} (- \frac{1}{2} σ_{ε} G_{2} [h, h])] :,$
X-F@1#eq:all-tree · line 958
$Φ^{F} (f) = ϕ (f) + κ A_{1} [h] + κ^{2} (Q [h, h] + A_{1} [k_{cl}] + T_{mat} + T_{mix} + T_{self}), h = h_{cl} + h .$