Manuscript XIII-B@1 · XIII-B.tex · section · b8a5c0f5

B3b: the joint two-line extension

B3b: the joint two-line extension · lines 914–932

XIII-B@1#eq:two-line

For regular kernels, the coefficient needed next is

R_{1}^{(1)}_{formal} = \frac{i}{2} ⟨ V_{g}^{''} \otimes O^{''}, H_{T}^{\otimes 2} - H^{\otimes 2} ⟩,

with the standard slot pairings and symmetrizations. Using (eq:HT), the difference contains

i (H \otimes G_{act}^{A} + G_{act}^{A} \otimes H) - G_{act}^{A} \otimes G_{act}^{A} .

The expression is a specification of contractions, not a proof that their joint product exists.

Displayed formulas in this passage

XIII-B@1#eq:two-line · line 918
$R_{1}^{(1)}_{formal} = \frac{i}{2} ⟨ V_{g}^{''} \otimes O^{''}, H_{T}^{\otimes 2} - H^{\otimes 2} ⟩,$
unlabeled · line 927
$i (H \otimes G_{act}^{A} + G_{act}^{A} \otimes H) - G_{act}^{A} \otimes G_{act}^{A} .$