The ongoing impact of modular localization on particle theory To the memory of Hans-Jurgen Borchers (1926-2011)

Abstract

dx.doi.org/10.7437/NF2318-4957/2013.01.002 Modular localization is the concise conceptual formulation of causal localizationin the setting of local quantum physics. Unlike QM it does not refer to individualoperators but rather to ensembles of observables which share the same localizationregion; as a result it explains the probabilistic aspects of QFT in terms of the impureKMS nature arising from the local restriction of the pure vacuum. Whereas it playsno important role in perturbation theory, as a result of representing the S-matrixas a relative modular invariant of wedge-localization it becomes indispensable forunderstanding analytic and algebraic properties of on-shell objects as the S-matrixand formfactors.This leads not only to a new critical evaluation of the dual model and string the-ory, but also identifies ideas of embedding and dimensional reduction as inconsistentwith the holistic properties of localization. Instead it reveals the conceptual originof true particle crossing and points the way to a new formulation of Mandelstam’son-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 ofrenormalizability for any spin.