Manuscript VI@1 · VI.tex · section · b5b60afb

The algebraic four-term identity

Second-order retarded bookkeeping and the missing quantum step › The algebraic four-term identity · lines 1847–1862

VI@1#eq:retarded-series

Let $R_{n}$ denote retarded products with the convention

R_{V} (F) = n = 0 \sum^{\infty} \frac{1}{n !} R_{n} (V^{\otimes n}; F), R_{0} (F) = F .

Suppose

V = κ V_{1} + κ^{2} V_{2}, F = O_{f}^{(0)} + κ O_{f}^{(1)} + κ^{2} O_{f}^{(2)} .

Displayed formulas in this passage

VI@1#eq:retarded-series · line 1850
$R_{V} (F) = n = 0 \sum^{\infty} \frac{1}{n !} R_{n} (V^{\otimes n}; F), R_{0} (F) = F .$
unlabeled · line 1858
$V = κ V_{1} + κ^{2} V_{2}, F = O_{f}^{(0)} + κ O_{f}^{(1)} + κ^{2} O_{f}^{(2)} .$