Particle Physics and QFT at the Turn of the Century Old principles with new concepts (an essay on local quantum physics)

TL;DR

This paper explores a novel perspective on quantum field theory using modular theory of von Neumann algebras, offering new insights into interactions, symmetries, and quantum measurement, with potential extensions to renormalization.

Contribution

It introduces a new framework for QFT based on modular theory, linking the S-matrix to modular invariants and providing a radical paradigm shift in understanding quantum interactions and measurement.

Findings

New modular approach to QFT interactions

Relation of S-matrix to modular invariants

Implications for quantum measurement theory

Abstract

The present state of QFT is analysed from a new viewpoint whose mathematical basis is the modular theory of von Neumann algebras. Its physical consequences suggest new ways of dealing with interactions, symmetries, Hawking-Unruh thermal properties and possibly also extensions of the scheme of renormalized perturbation theory. Interactions are incorporated by using the fact that the S-matrix is a relative modular invariant of the interacting- relative to the incoming- net of wedge algebras. This new point of view allows many interesting comparisions with the standard quantization approach to QFT and is shown to be firmly rooted in the history of QFT. Its radical ``change of paradigm'' aspect becomes particularily visible in the quantum measurement problem. Key words: Quantum Field Theory, S-matrix Theory, Tomita-Takesaki Modular Theory.