Topological sectors for Weyl-algebra net in the Einstein cylindrical universe

TL;DR

This paper constructs explicit topological cocycles for a massive bosonic quantum field theory on the Einstein cylinder, demonstrating their role in representing the fundamental group of the circle within algebraic quantum field theory.

Contribution

It provides explicit examples of topological cocycles in Roberts' net cohomology for quantum fields on the Einstein cylinder, advancing the understanding of topological sectors in algebraic QFT.

Findings

Constructed explicit topological cocycles for the Einstein cylinder

Demonstrated unitarily equivalent representations of the fundamental group

Extended algebraic framework for topological sectors in QFT

Abstract

This paper is an extended and more detailed version of arXiv:0812.0533. We tackle the problem of constructing explicit examples of topological cocycles of Roberts' net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum field theory on the two dimensional Einstein cylinder. After deriving some crucial results of the algebraic framework of quantization, we address the problem of the construction of the topological cocycles. All constructed cocycles lead to unitarily equivalent representations of the fundamental group of the circle (seen as a diffeomorphic image of all possible Cauchy surfaces).