Manuscript X-C@3 · X-C-v3.tex · definition · 2260f5f8

Definition: Test-level retarded M ller map

C2 and C3: maps, transposition, signs, and polarization · lines 681–700

X-C@3#def:moller, X-C@3#eq:moller, X-C@3#eq:second-map, X-C@3#eq:iteration

Define

R_{q} = (1 + L [q] E_{m}^{A})^{- 1} = 1 - κ L_{1, g} E_{m}^{A} + κ^{2} (L_{1, g} E_{m}^{A} L_{1, g} E_{m}^{A} - L_{2, g} E_{m}^{A}) .

For actual $c \in D (M)$ , the two missing maps are

R_{1} (V_{2, g}; F_{c}) \frac{1}{2} R_{2} (V_{1, g}, V_{1, g}; F_{c}) = ϕ (- L_{2, g} E_{m}^{A} c), = ϕ (L_{1, g} E_{m}^{A} L_{1, g} E_{m}^{A} c) .

The notation $\frac{1}{2} R_{2}$ names the second Taylor coefficient for the first vertex alone, not a general retarded product.

Displayed formulas in this passage

X-C@3#eq:moller · line 684
$R_{q} = (1 + L [q] E_{m}^{A})^{- 1} = 1 - κ L_{1, g} E_{m}^{A} + κ^{2} (L_{1, g} E_{m}^{A} L_{1, g} E_{m}^{A} - L_{2, g} E_{m}^{A}) .$
X-C@3#eq:second-map · line 691
$R_{1} (V_{2, g}; F_{c}) \frac{1}{2} R_{2} (V_{1, g}, V_{1, g}; F_{c}) = ϕ (- L_{2, g} E_{m}^{A} c), = ϕ (L_{1, g} E_{m}^{A} L_{1, g} E_{m}^{A} c) .$
X-C@3#eq:iteration · line 691
$R_{1} (V_{2, g}; F_{c}) \frac{1}{2} R_{2} (V_{1, g}, V_{1, g}; F_{c}) = ϕ (- L_{2, g} E_{m}^{A} c), = ϕ (L_{1, g} E_{m}^{A} L_{1, g} E_{m}^{A} c) .$