References

XB

N. Cheung. Landmark X-B: Fixed-regulator admission and one retarded correction for the ramp relational scalar, with the metric kept classical. Supplied manuscript X-B-v3.tex. Full text used. Objects: Premises prem:geometry–prem:scalar; Definition def:retarded; Theorems thm:retarded, thm:hbar, thm:ward; Propositions prop:joint, prop:linear, prop:zero; equations eq:Rone, eq:contraction-check, eq:off-shell-warning, eq:defect-class.

XA

N. Cheung. {Landmark X-A: Classical covariance of one fixed-regulator switched relational scalar through order ${\kappa }^2$}. Supplied manuscript X-A.tex. Used only through the premises copied in X-B.

FR

K. Fredenhagen and K. Rejzner. Perturbative algebraic quantum field theory. arXiv:1208.1428. Terminology for the free Wick presentation, the cone condition, and time-ordered products.

DF

M. Dütsch and K. Fredenhagen. Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity. Rev.\ Math.\ Phys. 16 (2004), 1291–1348. Terminology for retarded products and the $\hslash$/field-degree grading of renormalization terms.

BF

R. Brunetti and K. Fredenhagen. Microlocal analysis and interacting quantum field theories: renormalization on physical backgrounds. Comm.\ Math.\ Phys. 208 (2000), 623–661. Reference for the extension problem of products of Feynman-type kernels across diagonals; not opened here.

BGP

C. Bär, N. Ginoux, and F. Pfäffle. Wave Equations on Lorentzian Manifolds and Quantization. European Mathematical Society, 2007. Green operators, transposition, the Cauchy problem (Thm. 3.2.11), and spatially compact solutions as ${\Delta }_S\mathcal{D}$ (Thm. 3.4.7).

Hormander

L. Hörmander. The Analysis of Linear Partial Differential Operators I. Second edition. Springer, 1990. Wavefront set under differential operators (8.1.11), pullbacks (Thm. 8.2.4), products (Thm. 8.2.10), and kernels (Thm. 8.2.13).

Radzikowski

M. J. Radzikowski. Micro-local approach to the Hadamard condition in quantum field theory on curved space-time. Comm.\ Math.\ Phys. 179 (1996), 529–553. Wavefront set of Hadamard two-point distributions (Thm. 5.1).