Standard Subspaces and Modular Theory -- General Theory and Applications to QFT
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.
Related
- A modular theory of contractive projections on Banach spaces with applications to noncommutative Lp-spaces
- Automorphisms of general modular curves
- Free modules of vector-valued modular forms and applications to Jacobi forms
- An explicit form of the standard conjecture of Hodge type for Hermitian varieties, with p-adic applications
- Gromov-Witten theory of the local model of the standard flop
BibTeX
@misc{silva2026standard,
title = {{Standard Subspaces and Modular Theory -- General Theory and Applications to QFT}},
author = {Ricardo Correa da Silva and Gandalf Lechner and Roberto Longo},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08668},
eprint = {2611.08668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08668},
}
RIS
TY - UNPB
TI - Standard Subspaces and Modular Theory -- General Theory and Applications to QFT
AU - Ricardo Correa da Silva
AU - Gandalf Lechner
AU - Roberto Longo
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08668
UR - https://arxiv.org/abs/2611.08668
AB - 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.
ER -