References

XE

N. Cheung. Landmark X-E: A specified gravitational action for the ramp relational scalar, and the first graviton tree. Supplied manuscript X-E.tex.

XF

N. Cheung. {Landmark X-F: The second-order quantum metric as the retarded Moller response, and the closure of the ${\kappa }^2$ background identity}. Supplied manuscript X-F.tex.

BF

R. Brunetti and K. Fredenhagen. Microlocal analysis and interacting quantum field theories: renormalization on physical backgrounds. Communications in Mathematical Physics 208 (2000), 623–661. arXiv:math-ph/9903028. Used for the finite-scaling-degree extension theorem, not as a construction of the nonlocal mixed retarded product.

FR

K. Fredenhagen and K. Rejzner. Perturbative algebraic quantum field theory. arXiv:1208.1428v2, 2013. Background for polynomial Hadamard products, retarded products, and ordering equivalences.

HW

S. Hollands and R. M. Wald. Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes. Reviews in Mathematical Physics 17 (2005), 227–312. arXiv:gr-qc/0404074v2. Used to distinguish perturbative agreement from the preceding covariance and normalization conditions. Its scalar-field theorem is not imported as a graded gravitational completion.

TTZ

M. Taslimi Tehrani and J. Zahn. Background independence in gauge theories. Annales Henri Poincare 21 (2020), 1135. arXiv:1804.07640v3. Comparison for quantum background transport and possible obstructions. No anomaly-removal theorem for the present switched model is inferred.

BFR

R. Brunetti, K. Fredenhagen, and K. Rejzner. Quantum gravity from the point of view of locally covariant quantum field theory. Communications in Mathematical Physics 345 (2016), 741–779. arXiv:1306.1058. Comparison framework for locally covariant perturbative gravity and renormalized BV constructions. It does not identify source switching with density switching.

Hor

L. Hörmander. The Analysis of Linear Partial Differential Operators I, second edition. Springer, 1990. Used for the wavefront product and pushforward criteria. A failed sufficient product criterion is not used as a nonexistence theorem.