Vinck & De Haro (2026) redefine 'background-independent algebra' as representation-independence rather than dynamical spacetime

physicsphilosophy-of-physicsquantum-gravitybackground-independencealgebraic-qftsemiclassical-gravityhist-pharxiv

Having argued that no prior definition of background-independence captures Witten's claim for the CLPW algebra, Vinck & De Haro propose a new one that applies to an algebra rather than a full theory: an algebra is background-independent iff it can be interpreted as an abstract operator algebra making no reference to any spacetime structure, while still admitting a spacetime interpretation once a state or representation is chosen. This is an explicit departure from the three prior definitions the paper reviews — Anderson's absolute objects, Pooley's variational principle, and Belot's degrees-of-freedom proposal — all of which cash out background-independence in terms of the background itself being dynamical. Here the property attaches instead to representation-independence: the same abstract algebra, uninterpreted, can be represented against more than one classical background.

From this they derive two narrower, nested notions tailored to semiclassical gravity: "semiclassical background-independence" (the theory can be formulated for any classical background in the strict G → 0 limit) and "perturbative background-independence" (the stronger requirement that this survives once small G-corrections from backreaction are switched on).