Topological features of massive bosons on two dimensional Einstein space-time

TL;DR

This paper constructs explicit topological cocycles for massive bosonic quantum field theory on a 2D Einstein cylinder, linking algebraic quantum field theory with topological features of spacetime.

Contribution

It provides a novel explicit construction of topological cocycles in algebraic quantum field theory on curved spacetime, using only Cauchy data on the circle.

Findings

All cocycles lead to unitarily equivalent representations of the fundamental group.

Construction relies solely on Cauchy data and local algebras.

Advances understanding of topological aspects in quantum field theory on curved spacetime.

Abstract

In this paper 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). The construction is carried out using only Cauchy data and related net of local algebras on the circle.