Manuscript XI-B@1 · XI-B.tex · section · 063b989e

Ghost normalization and inverse

Causal Green operators and their normalization › Ghost normalization and inverse · lines 759–780

XI-B@1#eq:Gghost

Use left Grassmann variations. The ghost kinetic term yields

\frac{δ ^{L} S _{0}}{δ c} = - i □ c ˉ, \frac{δ ^{L} S _{0}}{δ c ˉ} = i □ c .

In the order $(c, c ˉ)$ , with dual vector indices understood,

L_{gh} = (0 i □ - i □ 0), G^{gh}^{\pm} = (0 i E_{0}^{\pm} - i E_{0}^{\pm} 0) .

Matrix multiplication proves the two Green identities. The scalar, auxiliary, and ghost blocks together give the full free multiplet Green operator. No Feynman inverse is selected.

Displayed formulas in this passage

XI-B@1#eq:Gghost · line 767
$L_{gh} = (0 i □ - i □ 0), G^{gh}^{\pm} = (0 i E_{0}^{\pm} - i E_{0}^{\pm} 0) .$
unlabeled · line 762
$\frac{δ ^{L} S _{0}}{δ c} = - i □ c ˉ, \frac{δ ^{L} S _{0}}{δ c ˉ} = i □ c .$