Manuscript Em01-B@3 · Em01-B-v3.tex · section · 69189992

Explicit vertex and its arbitrary-test action

Frozen expression and complete contraction › Explicit vertex and its arbitrary-test action · lines 602–622

Define the linear submersion

f (w) = (y - a, y - b) .

The symbol $\partial_{2, μ}$ differentiates only the second relative variable; $\partial_{2}^{ν} = η^{ν λ} \partial_{2, λ}$ .

For smooth $C$ , put

Z_{I}^{ν} (C) = f^{*} (\partial_{2, μ} C_{I}^{μν} - \frac{1}{2} η_{μ λ} \partial_{2}^{ν} C_{I}^{μ λ}), M_{I} (C) = f^{*} (η_{μν} C_{I}^{μν}) .

Displayed formulas in this passage

unlabeled · line 605
$f (w) = (y - a, y - b) .$
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$Z_{I}^{ν} (C) = f^{*} (\partial_{2, μ} C_{I}^{μν} - \frac{1}{2} η_{μ λ} \partial_{2}^{ν} C_{I}^{μ λ}), M_{I} (C) = f^{*} (η_{μν} C_{I}^{μν}) .$