Inclusions of Standard Subspaces
Ricardo Correa da Silva, Gandalf Lechner

TL;DR
This paper studies the structure and properties of inclusions of standard subspaces in Hilbert spaces, introducing new methods and analyzing examples from conformal field theory.
Contribution
It develops novel techniques for analyzing standard subspace inclusions, independent of von Neumann algebra frameworks, and explores examples from conformal field theory.
Findings
New methods related to polarizers and Gelfand triples are introduced.
Inclusions of standard subspaces are characterized independently of von Neumann algebras.
A detailed analysis of examples from conformal field theory is provided.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology
