Minimal coupling

In general relativity, the standard prescription for turning a special-relativistic field equation into a general-relativistic one by replacing ordinary partial derivatives with covariant derivatives relative to the spacetime metric — informally, "commas go to semicolons" — while introducing no new curvature-coupling terms.

Matters to this vault as the concept March and Weatherall's 2026 paper gives a precise category-theoretic definition for, the first time, proving that a minimal coupling in their exact sense is unique up to isomorphism where one exists — resolving a plurality the prescription had previously been thought to admit. The paper notes, as a nuance, that Einstein's own field equation is not minimally coupled under this precise definition, since it depends on the metric to second order rather than first.

References

• claim-march-weatherall-minimal-coupling-unique-up-to-isomorphism
• claim-march-weatherall-causal-cones-coincide-with-metric-lightcones
• claim-march-weatherall-natural-maximal-hyperbolizations-satisfy-dominant-energy-condition
• claim-march-weatherall-hyperbolization-tensor-divergence-free-by-naturality