The ongoing impact of modular localization on particle theory

Bert Schroer
February 07, 2013
Modular localization is the concise conceptual formulation of causal localization in the setting of local quantum physics. Unlike QM, it does not refer to individual operators but rather to ensembles of observables which share the same localization region; as a result it explains the probabilistic aspects of QFT in terms of the impure KMS nature arising from the local restriction of the pure vacuum. Whereas it plays no important role in perturbation theory, it becomes indispensable for understanding analytic and algebraic properties of on-shell objects as the S-matrix and formfactors. This leads not only to a new critical evaluation of the dual model and string theory, but also identifies ideas of embedding and dimensional reduction as inconsistent with the holistic properties of localization. Instead it reveals the conceptual origin of true particle crossing and points the way to a new formulation of Mandelstam's on-shell project of the 60s. Modular localization also shows that perturbative calculations in the Krein-space setting can be better done directly in Hilbert space with the help of short-distance lowering string-localized potentials. This points to a vast extension of renormalizability for any spin