On the Localization Properties of Quantum Field Theories with Infinite Spin

LQP 36 Foundations and Constructive Aspects of Quantum Field Theory
Christian Köhler on May 29, 2015

While pointlike localized free fields can be constructed for the positive mass and massless helicity representations of the Poincaré group, just string-localized fields are known to exist for the infinite spin case, the only remaining class of positive-energy representations. [Mund, Schroer, Yngvason 2006] There is even a No-Go Theorem on the existence of Wightman fields with infinite spin. [Yngvason 1970] However, two-particle wavefunctions with compact modular localization [Brunetti, Guido, Longo 2002] can in fact be constructed. In my talk I want to discuss results of my PhD project (Supervisor: Jakob Yngvason) regarding the construction of fields which create these wavefunctions from the vacuum: It turns out that they are incompatible with relative locality to the known string-localized fields due to the conflicting requirements of covariance and momentum-space analyticity. In addition, these incompatibilities are illustrated by a geometric construction which presents the string-localized fields as limits of their massive counterparts.