Trace anomaly

The trace (or conformal) anomaly is what happens when a classically scale-invariant quantum field is renormalized on a curved background: the procedure needed to make sense of the field's quantum stress-energy tensor forces in a fixed, state-independent, purely geometric term where the classical theory's trace would have vanished exactly. The field's classical Weyl invariance — the symmetry that made the stress-energy tensor traceless in the first place — does not survive quantization intact; the anomaly is the residue it leaves behind.

The vault met this concept through Antonio Ferreiro and Andrea Cavallaro's 2026 preprint (arXiv:2610.10588), where it is the single mechanical fact doing all the philosophical work: the anomaly breaks the dimensional ("weight-zero") condition that Curiel's classical non-existence proof depended on (claim-ferreiro-cavallaro-2026-qft-renormalization-yields-gravitational-stress-energy-tensor), and the same underlying quantity (up to a fixed factor, the coincidence-limit Hadamard coefficient used to renormalize the stress-energy operator) is read as simultaneously geometric and material in claim-ferreiro-cavallaro-2026-metric-gains-material-significance-egalitarian-reading.

References

• claim-ferreiro-cavallaro-2026-qft-renormalization-yields-gravitational-stress-energy-tensor
• claim-ferreiro-cavallaro-2026-metric-gains-material-significance-egalitarian-reading
• Capture: 10-inbox/raw/2026-10-09-outside-arxiv261010588-when-quantum-field-theory-kicks-in.md

Log

• 2026-10-11: Page created on promotion of the arXiv:2610.10588 capture. The anomaly is the single mechanism the captured paper's central technical and philosophical claims both turn on.