The Pivotal Role of Causality in Local Quantum Physics

TL;DR

This paper explores how causality and modular theory underpin recent advances in local quantum physics, offering new geometric insights and computational methods for nonperturbative quantum field theory.

Contribution

It demonstrates the application of Tomita's modular theory to connect quantum algebraic structures with classical geometry, advancing nonperturbative QFT techniques.

Findings

Modular theory provides a geometric framework for local quantum physics.

Causality principles underpin new computational approaches in QFT.

The approach offers potential for nonperturbative quantum field calculations.

Abstract

In this article an attempt is made to present very recent conceptual and computational developments in QFT as new manifestations of old and well establihed physical principles. The vehicle for converting the quantum-algebraic aspects of local quantum physics into more classical geometric structures is the modular theory of Tomita. As the above named laureate to whom I have dedicated has shown together with his collaborator for the first time in sufficient generality, its use in physics goes through Einstein causality. This line of research recently gained momentum when it was realized that it is not only of structural and conceptual innovative power (see section 4), but also promises to be a new computational road into nonperturbative QFT (section 5) which, picturesquely speaking, enters the subject on the extreme opposite (noncommutative) side.