Manuscript XVI-J@1 · XVI-J.tex · section · 6c1f306d

Fiber contraction and normalization

Fiber contraction and normalization · lines 717–731

XVI-J@1#eq:edgefiber

The vertex Hessian is a covariant bilinear form on $V$ . A field derivative at either end of an edge is a covector in $V^{*}$ . The propagator takes such a covector to a field vector after the identification by $b^{- 1}$ . Its fiber tensor, with the scalar factor $S$ removed, is

E = (- P \otimes id) b^{- 1} = i \sum Z_{i} \otimes B_{i}, Z_{i} = - P B^{i} .

Displayed formulas in this passage

XVI-J@1#eq:edgefiber · line 724
$E = (- P \otimes id) b^{- 1} = i \sum Z_{i} \otimes B_{i}, Z_{i} = - P B^{i} .$

Nearby in this section

section: Fiber contraction and normalization
lemma: Lemma: Gram matrix and inverse pairing
definition: Definition: Source-decorated tensor
proposition: Proposition: Basis independence and graph factor
section: Fiber contraction and normalization