Placing hidden properties of quantum field theory into the forefront: wedge localization and a new constructive on-shell setting

TL;DR

This paper explores modular localization in quantum field theory, revealing new non-perturbative methods, deriving particle crossing from KMS states, and connecting wedge localization with the Zamolodchikov-Faddeev algebra, aiming for a Hilbert space formulation without BRST.

Contribution

It introduces a novel constructive approach based on wedge localization and modular theory, extending to non-integrable models and higher spin fields, avoiding traditional gauge methods.

Findings

Derived particle crossing from KMS states in wedge-localized algebras.

Connected wedge localization with Zamolodchikov-Faddeev algebraic structures.

Proposed a Hilbert space formulation for higher spin fields avoiding BRST.

Abstract

Recent progress about "modular localization" reveals that, as a result of the S-Matrix in its role of a "relative modular invariant of wedge-localization, one obtains a new non-perturbative constructive setting of local quantum physicis which only uses intrinsic (independent of quantization) properties. The main point is a derivation of the particle crossing property from the KMS identity of wedge-localized subalgebras in which the connection of incoming/outgoing particles with interacting fields is achieved by "emulation" of free wedge-localized fields within the wedge-localized interacting algebra. The suspicion that the duality of the meromorphic functions, which appear in the dual model, are not related with particle physics, but are rather the result of Mellin-transforms of global operator-product expansions in conformal QFT is thus confirmed. The connection of the wedge-localization setting with the Zamolodchikov-Faddeev algebraic structure is pointed out and an Ansatz for an extension to non-integrable models is presented. Modular localization leads also to a widening of the renormalized perturbation setting by allowing couplings of string-localized higher spin fields which stay within the power-counting limit. This holds the promise of a Hilbert space formulation which avoids the use of BRST Krein-spaces. .