Two principles of decoupling

Abstract

We put forward a radial principle and a degeneracy locating principle of decoupling. The former generalises the Pramanik-Seeger argument used in the proof of decoupling for the light cone. The latter locates the degenerate part of a manifold and effectively reduces the decoupling problem to two extremes: non-degenerate case and totally degenerate case. Both principles aim to provide a new algebraic approach of reducing decoupling for new manifolds to decoupling for known manifolds.

v2: major modification to v1 to adapt to [arXiv:2407.16108] v3: minor modification to v2 to adapt to [arXiv:2507.02134]