Geometry and Localization, a metaphorically related pair

TL;DR

This paper explores the intrinsic localization structures in quantum field theory, contrasting them with geometric metaphors, and introduces modular localization as a new nonperturbative approach with recent existence theorems for certain QFTs.

Contribution

It highlights the importance of quantum localization over geometric metaphors and presents the first existence theorems for a class of renormalizable factorizable QFTs based on modular localization.

Findings

Quantum localization can differ from geometric ideas in QFT.

Modular localization offers a new nonperturbative framework for QFT.

Existence theorems established for certain renormalizable factorizable QFTs.

Abstract

It is often overlooked that local quantum physics has a built in quantum localization structure which may under certain circumstances disagree with (differential, algebraic) geometric ideas. String theory originated from such a spectacular misinterpretation of a source-target embedding in which an inner symmetry of the source object becomes the Lorentz symmetry of the target space. The quantum localization reveals however that the resulting object is an infinite component pointlike field. There are also other other areas in QFT which suffered from having followed geometrical metaphors and payed too little attention to the autonomous localization properties. This will be illustrated in the concrete context of three examples. We also show that "modular localization ", i.e. the intrinsic localization theory of local quantum quantum physics, leads to a radiacal new way of looking at (nonperturbative) QFT. For the first time in the history of QFT there are now existence theorems for a class of strictly renormalizable (i.e. not superrenormalizable) factorizable QFTs which are based on these new concepts. The paper ends with some worrisome sociological observations about the state of particle physics and the direction in which it is heading. These remarks are based on the results presented in the three previous sections.