HomeAbstract
Was
von Neumann Right After All?
Introduction
Philosophical ideas behind von Neumann algebras
Von Neumann, Dirac, and Feynman
Hyperfinite factors in quantum TGD
Hyperfinite factors and Mmatrix
Connes tensor product as a realization of a finite measurement resolution
Quantum spinors and fuzzy quantum mechanics
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 II
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 infinitedimensional configuration
space of 3surfaces
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 HFFs can one imagine in TGD?
Direct sum of HFFs of type II_{1} as minimum 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
Configuration space, spacetime, and imbedding space and hyperfinite type II_{1} factors
Quaternions, octonions, and hyperfinite type II_{1} factors
Does the hierarchy of infinite primes relate to the hierarchy of II_{1} factors?
Could HFFs of type III_{1} 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 the II_{∞} automorphism defining factor of type III?
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}_{+/} degrees of freedom?
Could the continuation of braidings to homotopies involve Δ^{it} automorphisms
HFFs of type III as superstructures providing additional uniqueness?
The latest vision about the role of HFFs in TGD
Basic facts about factors
Inclusions and Connes tensor product
Factors in quantum field theory and thermodynamics
TGD and factors
Can one identify Mmatrix from physical arguments?
Finite measurement resolution and HFFs
Questions about quantum measurement theory in zero energy ontology
How padic coupling constant evolution and padic length scale hypothesis emerge from quantum TGD proper?
Some speculations related to the role of HFFs in TGD
Planar algebras and generalized Feynman diagrams
Miscellaneous
Jones inclusions and cognitive consciousness
Does one have a hierarchy of
M and Umatrices?
Feynman diagrams as higher level particles and their scattering as dynamics of self consciousness
Logic, beliefs, and spinor fields in the world of classical worlds
Jones inclusions for hyperfinite factors of type II_{1} as a model for symbolic and cognitive representations
Intentional comparison of beliefs by topological quantum computation?
The stability of fuzzy qbits and quantum computation
Fuzzy quantum logic and possible anomalies in the
experimental data for the EPRBohm experiment
Category theoretic formulation for quantum measurement theory with finite measurement
resolution
Appendix

About inclusions of
hyperfinite factors of type II_{1}

Generalization from SU(2) to arbitrary compact group
