Classical pullback versus quantum substitution

The coefficients in Section sec:classical come from a classical Taylor expansion of $N_s\circ {\alpha }_s$. If a classical configuration is small enough that the clock-and-rod map is invertible, its fixed inverse ${\alpha }_s$ is an ordinary diffeomorphism. Distributional pullback by that fixed map is allowed by D2.

For a fixed spacelike slice embedding, the conormal covectors are timelike. A free normally hyperbolic solution with null wavefront set can therefore be restricted to that slice. The corresponding simultaneous equal-time restriction of $W$ also exists.

Neither assertion defines

A field-dependent quantum substitution requires the products appearing in its expansion. In this manuscript its retained jet is represented only by (eq:ncomplete) with the specified Wick and extension rules.