Manuscript XV-C@1 · XV-C.tex · section · 5afd124d

The unchanged pole

Frozen branch and placement ledger › The unchanged pole · lines 374–397

XV-C@1#eq:pole

The supplied internal pole chart is

M_{R} = - \frac{s}{2 ρ} (ω - s ρ - i 0)^{- 1} + \frac{s}{2 ρ ( ω + s ρ )}, ρ > 0, ∣ ω - s ρ ∣ < c ρ, 0 < c < 1,

with $s \in {+ 1, - 1}$ and

(λ - i 0)^{- 1} = PV \frac{1}{λ} + iπ δ (λ) .

It represents the existing retarded line Ipole. Its delta part is not adjusted in this manuscript. No graph regulator, finite-part prescription, or restoring limit is introduced.

Displayed formulas in this passage

XV-C@1#eq:pole · line 377
$M_{R} = - \frac{s}{2 ρ} (ω - s ρ - i 0)^{- 1} + \frac{s}{2 ρ ( ω + s ρ )}, ρ > 0, ∣ ω - s ρ ∣ < c ρ, 0 < c < 1,$
unlabeled · line 388
$(λ - i 0)^{- 1} = PV \frac{1}{λ} + iπ δ (λ) .$