Manuscript XI-E@1 · XI-E.tex · definition · 46e55514

Definition: Polynomial microcausal domain

Route 1: a named polynomial Hadamard extension › The polynomial domain and product · lines 697–714

XI-E@1#def:domain, XI-E@1#eq:mc

Let $F_{mc, pol}$ consist of finite graded polynomials

F (Φ) = n = 0 \sum^{N} ⟨ u_{n}, Φ^{\otimes n} ⟩,

where the kernels are compact, graded symmetric distributions on $M^{n}$ , with finite field indices, and satisfy

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

The cones include zero covectors; a total zero covector is never a wavefront point. Define $F_{mc, pol}^{sol}$ by restriction to the linear solution space (eq:shell).

Displayed formulas in this passage

XI-E@1#eq:mc · line 705
$WF (u_{n}) \cap (V_{+}^{n} \cup V_{-}^{n}) = \emptyset .$
unlabeled · line 700
$F (Φ) = n = 0 \sum^{N} ⟨ u_{n}, Φ^{\otimes n} ⟩,$

Nearby in this section

section: The polynomial domain and product
theorem: Theorem: Existence and on-shell descent
section: The polynomial domain and product