HomeAbstract
Was
von Neumann Right After All?
Introduction
Philosophical ideas behind von Neumann algebras
Von Neumann, Dirac, and Feynman
Von Neumann algebras
Basic definitions
Basic classification of von Neumann algebras
Noncommutative measure theory and noncommutative topologies and geometries
Modular automorphisms
Joint modular structure and sectors
Basic facts about hyperfinite factors of type III
Braid group, von Neumann algebras, quantum TGD, and formation of bound states
Factors of von Neumann algebras
Subfactors
II_{1} factors and the spinor structure of WCW
About possible spacetime correlates for the hierarchy of II_{1} subfactors
Could binding energy spectra reflect the hierarchy of effective tensor factor dimensions?
Fourcolor problem,II_{1} factors, and anyons
Inclusions of II_{1} and III_{1} factors
Basic findings about inclusions
The fundamental construction and TemperleyLieb algebras
Connection with Dynkin diagrams
Indices for the inclusions of type III_{1} factors
TGD and hyperfinite factors of type II_{1}: ideas and questions
What kind of hyperfinite factors one can imagine in TGD?
Direct sum of HFFs of type II_{1}as a minimal option
Bott periodicity, its generalization, and dimension D=8 as an inherent property of the hyperfinite II_{1} factor
The interpretation of Jones inclusions in TGD framework
WCW , spacetime, and imbedding space and hyperfinite type II_{1} factors
Quaternions, octonions, and hyperfinite typeII_{1} factors
Does the hierarchy of infinite primes relate to the hierarchy of II_{1} factors?
Could HFFs of type II have application in TGD framework?
Problems associated with the physical interpretation of III_{1} factors
Quantum measurement theory and HFFs of type III
What could one say about II_{1} automorphism associated with II^{∞? }
What could be the physical interpretation of two kinds of invariants associated with HFFs type III?
Does the time parameter t represent time translation or scaling?
Could HFFs of type III be associated with the dynamics in M^{4}_{+/× CP2? }
Could the continuation of braidings to homotopies involve Δ^{it}?
HFFs of type $III$ as superstructures providing additional uniqueness?
Appendix: Inclusions of hyperfinite factors of type II_{1}
Jones inclusions
Wassermann's inclusion
Generalization from SU(2) to arbitrary compact group
