Manuscript X-L-ST@1 · X-L-ST.tex · section · 20a32a22

The free causal carrier

The normalized free auxiliary–ghost package › The free causal carrier · lines 565–592

X-L-ST@1#eq:freeeq, X-L-ST@1#eq:CCR

Put

δ_{m} = E_{m}^{R} - E_{m}^{A}, Δ_{0} = G_{0}^{R} - G_{0}^{A} .

The free equations are

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

Define $A_{0}$ over $C [[ℏ]]$ by compactly smeared linear fields, equations (eq:freeeq), and the graded causal relations

[Φ_{A} (f), Φ_{B} (g)]_{gr} = i ℏ ⟨ f, Δ_{0, A B} g ⟩ 1 .

Only finite polynomial products are used. No coincident nonlinear Wick field is included by this definition.

Displayed formulas in this passage

X-L-ST@1#eq:freeeq · line 575
$A r + C^{*} b = 0, C r - 2 b = 0, P_{m} ϕ = 0, □ c = □ c ˉ = 0.$
X-L-ST@1#eq:CCR · line 584
$[Φ_{A} (f), Φ_{B} (g)]_{gr} = i ℏ ⟨ f, Δ_{0, A B} g ⟩ 1 .$
unlabeled · line 568
$δ_{m} = E_{m}^{R} - E_{m}^{A}, Δ_{0} = G_{0}^{R} - G_{0}^{A} .$