Inclusions of Standard Subspaces

Correa da Silva R, Lechner G (2025)

Publication Language: English

Publication Status: In review

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2025

URI: https://arxiv.org/abs/2506.16085

Abstract

Standard subspaces are closed real subspaces of a complex Hilbert space that appear naturally in Tomita-Takesaki modular theory and its applications to quantum field theory. In this article, inclusions of standard subspaces are studied independently of von Neumann algebras. Several new methods for their investigation are developed, related to polarizers, Gelfand triples defined by modular data, and extensions of modular operators. A particular class of examples that arises from the fundamental irreducible building block of a conformal field theory on the line is analyzed in detail.

Authors with CRIS profile

Ricardo Correa da Silva Lehrstuhl für Mathematik (Algebra und Geometrie) Gandalf Lechner Lehrstuhl für Mathematik (Operatoralgebren) (Heisenberg-Professur)

How to cite

APA:

Correa da Silva, R., & Lechner, G. (2025). Inclusions of Standard Subspaces. (Unpublished, In review).

MLA:

Correa da Silva, Ricardo, and Gandalf Lechner. Inclusions of Standard Subspaces. Unpublished, In review. 2025.

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