Remarks on the Reeh-Schlieder property for higher spin free fields on curved spacetimes
type: Item
instance of: scholarly article
zbMATH Open document ID: 1260.81186
DOI: 10.1142/S0129055X11004515
author: Claudio Dappiaggi
published in: Reviews in Mathematical Physics
publication date: 2012-06-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1102.5270
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 81T05
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 46L60
zbMATH DE Number: 6045731
zbMATH Keywords: Quantum field theory on curved space-times
zbMATH Keywords: Reeh-Schlieder states
zbMATH Keywords: Dirac field
zbMATH Keywords: Proca field
zbMATH Keywords: Higher spin field theories
MaRDI profile type: Publication
arXiv ID: 1102.5270
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title: Remarks on the Reeh-Schlieder property for higher spin free fields on curved spacetimes
review text: One of the main results in the algebraic approach to quantum field theory is the so-called Reeh-Schlieder theorem, which asserts that, in the framework of a real scalar field theory on Minkowski space-time, the set of vectors generated from the vacuum by the polynomial algebra of any open region is dense in the underlying Hilbert space. The main goal of the author is to prove that the existence of a state enjoying at least on a suitable region the Reeh-Schlieder property is not restricted to the example of a scalar field theory, but it can be extended to higher spin field theories, most notably the Dirac field, the Proca field and the vector potential. On the other hand, the author proves that the Dirac and the Proca field as well as the vector potential admit even on a generic globally hyperbolic space-time a state which enjoys the Reeh-Schlieder property at least on a suitable open region. To get to this result the author also shows that spin-\(1\) fields can be described as locally covariant quantum field theories regardless of the gauge freedom present in the massless case.
reviewed by: Stepan Moskaliuk
description: scientific article; zbMATH DE number 6045731