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

Second-order interacting bookkeeping

Second-order retarded bookkeeping and the missing quantum step › Coupling order is not loop order · lines 2005–2027

VI@1#fig:VI-four-term-prerequisites

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metric / coordinatescalarswitching defectconditional quantumsupport / uncompleted
Of(2)\mathcal O_f^{(2)}
R1(V1;Of(1))R_1(V_1;\mathcal O_f^{(1)})
kernel G□,0D(h)G_{\Box,0}D(h)
R1(V2;Of(0))R_1(V_2;\mathcal O_f^{(0)})
12R2(V1,V1;Of(0))\tfrac12 R_2(V_1,V_1;\mathcal O_f^{(0)})
needs T2(V1,V1)T_2(V_1,V_1) and the three-insertion product
conditional on product existence
[RV(F)]κ2[R_V(F)]_{\kappa^2}
required inputs: gravity, matter, ghost, and gauge fixing
κ2\kappa^2 does not specify loop order. Three fixed-state connected two-point terms; state variations add more.

Second-order interacting bookkeeping. Four terms contribute to the one-insertion coefficient, conditional on the required retarded products. Two-vertex products and products involving coordinate kernels are prerequisites, not consequences of the algebraic expansion. Coupling order does not determine loop order, and a two-point response requires additional product and state specifications.

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