Manuscript III@2 · III.tex · section · 82dad3e5

Spatial Poisson compensation

The unchanged free-product obstruction › Spatial Poisson compensation · lines 664–679

III@2#eq:Poisson-functional

For real $f \in C_{c}^{\infty} (M)$ , put

F^{P}_{0} (f; h, ϕ) F^{P}_{1} (f; h, ϕ) F^{P}_{κ} (f; h, ϕ) = \int_{M} f ϕ d^{4} x, = \int_{M} f w_{P}^{μ} (h) \partial_{μ} ϕ d^{4} x, = F^{P}_{0} (f; h, ϕ) + κ F^{P}_{1} (f; h, ϕ) .

The displayed expression is an exact degree-one polynomial, not an all-orders invariant.

Displayed formulas in this passage

III@2#eq:Poisson-functional · line 667
$F^{P}_{0} (f; h, ϕ) F^{P}_{1} (f; h, ϕ) F^{P}_{κ} (f; h, ϕ) = \int_{M} f ϕ d^{4} x, = \int_{M} f w_{P}^{μ} (h) \partial_{μ} ϕ d^{4} x, = F^{P}_{0} (f; h, ϕ) + κ F^{P}_{1} (f; h, ϕ) .$