The Bisognano-Wichmann Theorem for Massive Theories

2001/01/31 by Jens Mund · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Black Holes and Theoretical Physics #Class (philosophy) #Covariant transformation #Epistemology #Geometry #Interpretation (philosophy) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Philosophy #Physics #Property (philosophy) #Pure mathematics #Theoretical physics #Wedge (geometry) #hep-th #math-ph #math.MP

paper · pdf · doi:10.1007/s00023-001-8598-x

published as Annales Henri Poincare 2 (2001) 907-926 · 16 pages; improved and corrected formulations

arxiv created 2001/02/22 · openalex publication_date 2001/10/01 · arxiv updated 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The geometric action of modular groups for wedge regions (Bisognano-Wichmann property) is derived from the principles of local quantum physics for a large class of Poincare covariant models in d=4. As a consequence, the CPT theorem holds for this class. The models must have a complete interpretation in terms of massive particles. The corresponding charges need not be localizable in compact regions: The most general case is admitted, namely localization in spacelike cones.

Citations

• Modular Covariance and the Algebraic PCT/Spin-Statistics Theorem
• Natural Energy Bounds in Quantum Thermodynamics
• On modular inclusion and spectrum condition
• Locality and the structure of particle states
• Modular structure and duality in conformal quantum field theory

Cited by

• The role of positivity and causality in interactions involving higher spin
• Pascual Jordan, his contributions to quantum mechanics and his legacy in contemporary local quantum physics