Manuscript VII-I@1 · VII-I.tex · section · 907e96ab

The sharp kernel and the off-shell admission obstruction

The sharp kernel and the off-shell admission obstruction · lines 505–529

Let $P_{mc, pol}$ be the finite polynomial space with compact, species-symmetric kernels $u_{n}$ satisfying

WF (u_{n}) \cap (V_{+}^{n} \cup V_{-}^{n}) = \emptyset,

where each cone contains its zero covector and the total zero covector is omitted.

For a linear coordinate test $a_{μ} \in C_{c}^{\infty} (M_{+}^{\circ})$ , put

ℓ_{a} [h] = \int a_{μ} (E_{0} C h)^{μ}, b = E^{A}_{0} a .

The formal adjoint of $C$ is

(C^{*} b)^{α β} = - \partial^{(α} b^{β)} + \frac{1}{2} η^{α β} \partial^{μ} b_{μ} .

Displayed formulas in this passage

unlabeled · line 510
$WF (u_{n}) \cap (V_{+}^{n} \cup V_{-}^{n}) = \emptyset,$
unlabeled · line 520
$ℓ_{a} [h] = \int a_{μ} (E_{0} C h)^{μ}, b = E^{A}_{0} a .$
unlabeled · line 524
$(C^{*} b)^{α β} = - \partial^{(α} b^{β)} + \frac{1}{2} η^{α β} \partial^{μ} b_{μ} .$