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Manuscript Em01-F@3 · Em01-F-v3.tex · section · 225e59af

Translation identity and reconstruction-null test

Translation identity and reconstruction-null test · lines 3149–3181

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For compact $Φ$ , define compact relative distributions

a_{I, ν} [Φ] = f_{*} (J \sum g (y) \partial_{y^{ν}} Φ_{J} K^{I, J}), d_{I} [Φ] = f_{*} (J \sum g (y) Φ_{J} K^{I, J}),

Λ_{I, μν} [Φ] = \frac{i}{2} (\partial_{2, μ} a_{I, ν} + \partial_{2, ν} a_{I, μ}) - \frac{i}{2} η_{μν} \partial_{2}^{ρ} a_{I, ρ} - \frac{i m ^{2}}{2} η_{μν} d_{I} .

With $d (x, v) = x - v$ , put

Ω_{Φ} = I, μ, ν \sum d_{*} (Λ_{I, μν} [Φ] \otimes χ C_{I}^{μν}) .

Displayed formulas in this passage

unlabeled · line 3153
$a_{I, ν} [Φ] = f_{*} (J \sum g (y) \partial_{y^{ν}} Φ_{J} K^{I, J}), d_{I} [Φ] = f_{*} (J \sum g (y) Φ_{J} K^{I, J}),$
unlabeled · line 3163
$Λ_{I, μν} [Φ] = \frac{i}{2} (\partial_{2, μ} a_{I, ν} + \partial_{2, ν} a_{I, μ}) - \frac{i}{2} η_{μν} \partial_{2}^{ρ} a_{I, ρ} - \frac{i m ^{2}}{2} η_{μν} d_{I} .$
unlabeled · line 3174
$Ω_{Φ} = I, μ, ν \sum d_{*} (Λ_{I, μν} [Φ] \otimes χ C_{I}^{μν}) .$

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