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

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.

41 pages, title changed, minor changes, typos corrected, references added. Accepted for publication in Ann. Henri Poincare'

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• The K-homology of nets of C*-algebras
• Representations of nets of C*-algebras over S^1
• Background potentials and superselection sectors