arXiv:2611.08668v1 Announce Type: new Abstract: This is a preview of an upcoming monograph on standard subspaces and modular theory. At the moment, it consists of the first chapter. This starts with a gentle introduction to the subject, and then describes the modular theory of standard subspaces, the characterization of their modular data by the KMS condition and reflection positivity, and various constructions of standard subspaces. Further topics in Chapter 1 include the connection of standard subspaces to complexifications and symplectic structures, including their polarizers, and operations with standard subspaces, namely direct sums, direct integrals, and tensor products. Many examples and classification results are included as well. This first chapter also contains a description of the free U(1)-current and some other applications to quantum field theory, such as KMS states of type I factors, the local subspaces of the free Klein--Gordon field, and the entropy operator defined by a standard subspace.
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