String-localized quantum fields, modular localization, and gauge theories

Abstract

The concept of modular localization intoduced by Brunetti, Guido and Longo, and Schroer, can be used to construct quantum fields. It combines Wigner's particle concept with the Tomita-Takesaki modular theory of operator algebras. I report on the construction of free fields which are localized in semi-infinite strings extending to spacelike infinity (joint work with B. Schroer and J. Yngvason). Particular applications are: The first local (in the above sense) construction of fields for Wigner's massless "infinite spin" particles; String-localized vector/tensor potentials for Photons and Gravitons, respectively; Massive vector bosons. Some speculative ideas will be presented concerning the perturbative construction of gauge theories (and quantum gravity) completely within a Hilbert space, trading gauge dependence with dependence on the direction of the localization string.