Localization in Nets of Standard Spaces

Lechner G, Longo R (2015)

Publication Type: Journal article

Publication year: 2015

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Book Volume: 336

Pages Range: 27-61

Journal Issue: 1

DOI: 10.1007/s00220-014-2199-2

Abstract

Starting from a real standard subspace of a Hilbert space and a representation of the translation group with natural properties, we construct and analyze for each endomorphism of this pair a local, translationally covariant net of standard subspaces, on the lightray and on two-dimensional Minkowski space. These nets share many features with low-dimensional quantum field theory, described by corresponding nets of von Neumann algebras.Generalizing a result of Longo and Witten to two dimensions and massive multiplicity free representations, we characterize these endomorphisms in terms of specific analytic functions. Such a characterization then allows us to analyze the corresponding nets of standard spaces, and in particular to compute their minimal localization length. The analogies and differences to the von Neumann algebraic situation are discussed.

Authors with CRIS profile

Gandalf Lechner

Additional Organisation(s)

Lehrstuhl für Mathematik (Operatoralgebren)

Involved external institutions

Università degli Studi di Roma 'Tor Vergata' IT Italy (IT) Universität Leipzig DE Germany (DE)

How to cite

APA:

Lechner, G., & Longo, R. (2015). Localization in Nets of Standard Spaces. Communications in Mathematical Physics, 336(1), 27-61. https://doi.org/10.1007/s00220-014-2199-2

MLA:

Lechner, Gandalf, and Roberto Longo. "Localization in Nets of Standard Spaces." Communications in Mathematical Physics 336.1 (2015): 27-61.

BibTeX: Download