Manuscript XIV-A@1 · XIV-A.tex · section · 71020abe

The relative differential of the observable is the pairing

A2: the observable ledger › The relative differential of the observable is the pairing · lines 1115–1128

XIV-A@1#eq:sextO

Since $O$ depends on $(γ, ϕ)$ only and is antifield-independent,

s_{ext} O = (S_{ext}, O) = ⟨ O^{'}_{γ}, s γ ⟩ + ⟨ O^{'}_{ϕ}, s ϕ ⟩ = s_{0} O + \frac{κ}{2} [⟨ O^{'}_{γ}, L_{c} γ ⟩ + ⟨ O^{'}_{ϕ}, c^{μ} \partial_{μ} ϕ ⟩], s_{0} O := ⟨ O^{'}_{γ}, R c ⟩ .

Displayed formulas in this passage

XIV-A@1#eq:sextO · line 1119
$s_{ext} O = (S_{ext}, O) = ⟨ O^{'}_{γ}, s γ ⟩ + ⟨ O^{'}_{ϕ}, s ϕ ⟩ = s_{0} O + \frac{κ}{2} [⟨ O^{'}_{γ}, L_{c} γ ⟩ + ⟨ O^{'}_{ϕ}, c^{μ} \partial_{μ} ϕ ⟩], s_{0} O := ⟨ O^{'}_{γ}, R c ⟩ .$