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<p>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.</p>

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Inclusions of Standard Subspaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月3日

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  • Ricardo Correa da Silva,
  • Gandalf Lechner

摘要

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.