Micro-Macro Duality in Quantum Physics

TL;DR

This paper explores the fundamental duality between microscopic quantum systems and macroscopic classical phenomena using categorical adjunctions, providing a unified framework for quantum measurement and superselection sectors applicable to quantum field theory.

Contribution

It introduces a categorical duality-based scheme unifying microscopic and macroscopic physics, extending superselection theory and measurement models to quantum field theory.

Findings

Unified framework for micro-macro relations via categorical adjunctions

Extension of superselection theory to systems with broken symmetries

Measurement scheme applicable to quantum field theory with type III von Neumann algebras

Abstract

Micro-Macro Duality means here the universal mutual relations between the microscopic quantum world and various macroscopic classical levels, which can be formulated mathematically as categorical adjunctions. It underlies a unified scheme for generalized sectors based upon selection criteria proposed by myself in 2003 to control different branches of physics from a unified viewpoint, which has played essential roles in extending the Doplicher-Haag-Roberts superselection theory to various situations with spontaneously as well as explicitly broken symmetries. Along this line of thought, the state correlations between a system and a measuring apparatus necessary for measurements can canonically be formulated within the context of group duality; the obtained measurement scheme is not restricted to the quantum mechanical situations with finite number of particles but can safely be applied to quantum field theory with infinite degrees of freedom whose local subalgebras are given by type III von Neumann algebras.