Manuscript IX-C-ST@1 · IX-C-ST.tex · section · 892f50c4

Covariance and old product

Shared analytical inputs and notation › Covariance and old product · lines 560–580

IX-C-ST@1#eq:Q, IX-C-ST@1#eq:Tself

These inputs retain the VII-C and IX-A-ST domain distinctions VIIC,IXAST; the functional microcausal convention is the one reviewed in FR. In particular $H_{w w} = 0$ does not imply $K = 0$ .

The selected already admitted comparison outputs are

Q_{f, g} T_{f, f^{'}} = - 2 ⟨ f (x) g (y) K (x, y), \partial_{t} ϕ (x) h_{00} (y) ⟩, = ⟨ f (x) f^{'} (x^{'}) S_{μν} (x, x^{'}), w^{μ} (x) w^{ν} (x^{'}) ⟩ .

Their admission is the explicit selected-output input in Assumption ass:carrier, not closure under an unspecified new contraction.

Displayed formulas in this passage

IX-C-ST@1#eq:Q · line 568
$Q_{f, g} T_{f, f^{'}} = - 2 ⟨ f (x) g (y) K (x, y), \partial_{t} ϕ (x) h_{00} (y) ⟩, = ⟨ f (x) f^{'} (x^{'}) S_{μν} (x, x^{'}), w^{μ} (x) w^{ν} (x^{'}) ⟩ .$
IX-C-ST@1#eq:Tself · line 568
$Q_{f, g} T_{f, f^{'}} = - 2 ⟨ f (x) g (y) K (x, y), \partial_{t} ϕ (x) h_{00} (y) ⟩, = ⟨ f (x) f^{'} (x^{'}) S_{μν} (x, x^{'}), w^{μ} (x) w^{ν} (x^{'}) ⟩ .$

Covariance and old product

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