Manuscript X-G@1 · X-G.tex · section · 01566e14

The causal algebra and its differential

The normalized free BRST multiplet › The causal algebra and its differential · lines 691–707

X-G@1#eq:freeeq

Define $A_{0}$ by compactly smeared linear fields, the equations

A h + C^{*} b = 0, C h - 2 b = 0, P_{m} ϕ = 0, □ c = □ c ˉ = 0,

and

[Φ_{A} (f), Φ_{B} (k)]_{gr} = i ℏ ⟨ f, Δ_{A B} k ⟩ 1 .

The graded causal form descends to the equation quotient. Its central graded Lie algebra has an enveloping algebra, providing the corresponding associative polynomial carrier.

Displayed formulas in this passage

X-G@1#eq:freeeq · line 694
$A h + C^{*} b = 0, C h - 2 b = 0, P_{m} ϕ = 0, □ c = □ c ˉ = 0,$
unlabeled · line 700
$[Φ_{A} (f), Φ_{B} (k)]_{gr} = i ℏ ⟨ f, Δ_{A B} k ⟩ 1 .$

Nearby in this section

theorem: Theorem: Free causal BRST differential