1999/12/22 by Dirk Schlingemann, Schlingemann, Dirk
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9912219
20 pages
arxiv created 1999/12/22 · openalex publication_date 1999/12/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The construction of the known interacting quantum field theory models is mostly based on euclidean techniques. The expectation values of interesting quantities are usually given in terms of euclidean correlation functions from which one should be able to extract information about the behavior of the correlation functions of the Minkowskian counterpart. We think that the C*-algebraic approach to euclidean field theory gives an appropriate setup in order to study structural aspects model independently. A previous paper deals with a construction scheme which relates to each euclidean field theory a Poincaré covariant quantum field theory model in the sense of R. Haag and D. Kastler. Within the framework of R. Haag and D. Kastler, the physical concept of PCT symmetry and spin and statistics is related to the Tomita-Takesaki theory of von Neumann algebras and this important aspects has been studied by several authors. We express the PCT symmetry in terms of euclidean reflexions and we explicitly identify the corresponding modular operator and the modular conjugation of the related Tomita-Takesaki theory. Locality, wedge duality, and a geometric action of the modular group of the von Neumann algebra of observables, localized within a wedge region in Minkowski space, are direct consequences.