Year: 2026
Type: article
Abstract: The Bisognano-Wichmann and Haag duality properties for algebraic quantum field theories are often studied using the powerful tools of Tomita-Takesaki modular theory for nets of operator algebras. In this article, we study analogous properties of nets of algebras generated by smeared Wightman fields, for potentially non-unitary theories. In light of recent work constructing Wightman field theories for (non-unitary) Möbius vertex algebras, we obtain a broadly applicable non-unitary version of the Bisognano-Wichmann property. In this setting we do not have access to the traditional tools of Hilbert space functional analysis, like functional calculus. Instead, results analogous to those of Tomita-Takesaki theory are derived ‘by hand’ from the Wightman axioms. As an application, we demonstrate Haag duality for nets of smeared Wightman fields.
Author: James E. Tener
Institution: Australian National University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Funder: Australian Research Council
OpenAlex ID: W4417354638
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