Superselectionrule and Observation Problems on Algebraic Quantum Field Theory

Furukawa T

Published on: 2022-12-01


On algebraic quantum field theory, I will focus on the sector theory, the representation theory of operator algebras (von Neumann algebras) related to it, and the relationship with the theory of irreducible decomposition.


Sector theory; Vacuum representation; Factor; Observation problem

General Issues of Sector Theory

A sector is, in the general framework of algebraic quantum field theory, “(the same class) superpositionable subspace sorted by a superselection rule (superselective charge)” [9]. Therefore, no superposition occurs between (vectors or representations of) two different sectors. In terms of the algebra of observables, sector can be described as the decomposition of the observable algebra (self-adjoint representation) into factor representations (irreducible decomposition representations) 1. Sectors are generally classified by discrete superselective charges (projections), so situations in which continuous superselective charges appear are not often assumed. However, from the standpoint of broadly understanding the order parameter, which is a macro-indicator used in thermodynamics and other fields, the problem of observation becomes clearer. Here, we will start with the general part.