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This Concept Map, created with IHMC CmapTools, has information related to: Hyperfinite factors and TGD.cmap, HYPERFINITE FACTORS AND TGD 4. Inclusions of HFFs allow to formulate the notion of finite measurement resolution in zero energy ontology, Inclusions of HFFs allow to formulate the notion of finite measurement resolution in zero energy ontology b) the included sub- factor creates states which cannot be distinguished in the resolution used, a projector with non-vanishing trace always projects to infinite-D subspace so that it is not possible to select a one- dimensional sub-space since the trace for the projector would vanish so that state function reduction is always to infinite sub-space with final state density matrix given by the projector, HYPERFINITE FACTORS AND TGD 2. Fermionic Fock space represents canonical example about hyper-finite factor of type II_1 (HFF), it is not possible to select a one- dimensional sub-space since the trace for the projector would vanish so that state function reduction is always to infinite sub-space with final state density matrix given by the projector raising the question how this degeneracy relates to the degeneracy unit density matrix assignable to negentropic entanglement associated with large h_eff hierarchy?, factors of type I appear in wave mechanics and lead to standard quantum measurement theory whereas hyper-finite factors of type III apppear in quantum field theory (von Neumann himself regarded these factors pathological), Fermionic Fock space represents canonical example about hyper-finite factor of type II_1 (HFF) and WCW spinors correspond to fermionic Fock space, HYPERFINITE FACTORS AND TGD 1. There are three types of core-HFF von Neuman algebras: HFF factors of type I,II,III?n, the trace of unit matrix equals to one rather than to infinite dimension of Hilbert space so that a projector with non-vanishing trace always projects to infinite-D subspace, WCW spinors correspond to fermionic Fock space which raises two questions Do WCW "orbital" degrees of freedom core- correspond to HFF by super-conformal symmetry?, it is not possible to select a one- dimensional sub-space since the trace for the projector would vanish so that state function reduction is always to infinite sub-space with final state density matrix given by the projector meaning that it is not possible to measure with complete precision: always infinite number of degrees of freedom remain unmeasured., There are three types of core-HFF von Neuman algebras: HFF factors of type I,II,III?n of which factors of type I appear in wave mechanics and lead to standard quantum measurement theory, characrterized by fractal dimensions (index of inclusion) characterizig the dimension of state space modulo finite measurement resolution giving connection with quantum groups, HFF is self-similar fractal in the sense that there is infinite hierarchy of inclusions of HFF to itself which are characrterized by fractal dimensions (index of inclusion) characterizig the dimension of state space modulo finite measurement resolution, Inclusions of HFFs allow to formulate the notion of finite measurement resolution in zero energy ontology a) HFF is self-similar fractal in the sense that there is infinite hierarchy of inclusions of HFF to itself, The basic properties of HFFs a) the trace of unit matrix equals to one rather than to infinite dimension of Hilbert space, HYPERFINITE FACTORS AND TGD 3. The basic properties of HFFs, WCW spinors correspond to fermionic Fock space which raises two questions Do WCW spinors correspond to HFF?, The basic properties of HFFs c) HFF can be approximated with finite-D sub-algebra in arbitrary accuracy, The basic properties of HFFs b) it is not possible to select a one- dimensional sub-space since the trace for the projector would vanish so that state function reduction is always to infinite sub-space with final state density matrix given by the projector
