Asymptotic Locality: Rectifying Newton--Wigner and Foldy--Wouthuysen Localization

Relativistic quantum theory supports two competing notions of particle locality. Newton--Wigner localization provides a sharp position operator on the one-particle Hilbert space but is not Lorentz covariant and leads to instantaneous spreading for positive-energy states. Foldy--Wouthuysen localization, widely used in precision experiments, yields a robust quasi-classical particle description but is representation-dependent and does not coincide with strict field-theoretic locality. We show that this tension is not a paradox in UV-complete nonlocal quantum field theories whose ultraviolet physics is encoded by an entire-function regulator. In such theories the physically accessible observables form a quasi-local algebra generated by regulated smearings with an intrinsic nonlocality length. Sharp Newton--Wigner projectors are not operationally realistic, and Newton--Wigner and Foldy--Wouthuysen localization become equivalent non-singular notions of locality in the same measurement algebra.