About some unclear issues of TGDTGD has been in the middle of palace revolution during last two years and it is almost impossible to keep the chapters of the books updated. Adelic vision and twistor lift of TGD are the newest developments and there are still many details to be understood and errors to be corrected. The description of fermions in TGD framework has contained some unclear issues. Hence the motivation for the following brief comments. Adelic vision and symmetries In the adelic TGD SH is weakened: also the points of the spacetime surface having imbedding space coordinates in an extension of rationals (cognitive representation) are needed so that data are not precisely 2D. I have believed hitherto that one must use preferred coordinates for the imbedding space H  a subset of these coordinates would define spacetime coordinates. These coordinates are determined apart from isometries. Does the number theoretic discretization imply loss of general coordinate invariance and also other symmetries? The reduction of symmetry groups to their subgroups (not only algebraic since powers of e define finitedimensional extension of padic numbers since e^{p} is ordinary padic number) is genuine loss of symmetry and reflects finite cognitive resolution. The physics itself has the symmetries of real physics. The assumption about preferred imbedding space coordinates is actually not necessary. Different choices of Hcoordinates means only different and nonequivalent cognitive representations. Spherical and linear coordinates in finite accuracy do not provide equivalent representations. Quantumclassical correspondence for fermions Quantumclassical correspondence (QCC) for fermions is rather wellunderstood but deserves to be mentioned also here. QCC for fermions means that the spacetime surface as preferred extremal should depend on fermionic quantum numbers. This is indeed the case if one requires QCC in the sense that the fermionic representations of Noether charges in the Cartan algebras of symmetry algebras are equal to those to the classical Noether charges for preferred extremals. Second aspect of QCC becomes visible in the representation of fermionic states as point like particles moving along the lightlike curves at the lightlike orbits of the partonic 2surfaces (curve at the orbit can be locally only lightlike or spacelike). The number of fermions and antifermions dictates the number of string world sheets carrying the data needed to fix the preferred extremal by SH. The complexity of the spacetime surface increases as the number of fermions increases. Strong form of holography for fermions It seems that scattering amplitudes can be formulated by assigning fermions with the boundaries of strings defining the lines of twistor diagrams. This information theoretic dimensional reduction from D=4 to D=2 for the scattering amplitudes can be partially understood in terms of strong form of holography (SH): one can construct the theory by using the data at string worlds sheets and/or partonic 2surfaces at the ends of the spacetime surface at the opposite boundaries of causal diamond (CD). 4D modified Dirac action would appear at fundamental level as supersymmetry demands but would be reduced for preferred extremals to its 2D stringy variant serving as effective action. Also the value of the 4D action determining the spacetime dynamics would reduce to effective stringy action containing area term, 2D Kähler action, and topological Kähler magnetic flux term. This reduction would be due to the huge gauge symmetries of preferred extremals. Subalgebra of supersymplectic algebra with conformal weigths coming as nmultiples of those for the entire algebra and the commutators of this algebra with the entire algebra would annihilate the physical states, and thecorresponding classical Noether charges would vanish. One still has the question why not the data at the entire string world sheets is not needed to construct scattering amplitudes. Scattering amplitudes of course need not code for the entire physics. QCC is indeed motivated by the fact that quantum experiments are always interpreted in terms of classical physics, which in TGD framework reduces to that for spacetime surface. The relationship between spinors in spacetime interior and at boundaries between Euclidian and Minkoskian regions Spacetime surface decomposes to interiors of Minkowskian and Euclidian regions. At lightlike 3surfaces at which the fourmetric changes, the 4metric is degenerate. These metrically singular 3surfaces  partonic orbits carry the boundaries of string world sheets identified as carriers of fermionic quantum numbers. The boundaries define fermion lines in the twistor lift of TGD. The relationship between fermions at the partonic orbits and interior of the spacetime surface has however remained somewhat enigmatic. So: What is the precise relationship between induced spinors Ψ_{B} at lightlike partonic 3surfaces and Ψ_{I} in the interior of Minkowskian and Euclidian regions? Same question can be made for the spinors Ψ_{B} at the boundaries of string world sheets and Ψ_{I} in interior of the string world sheets. There are two options to consider:
I have considered Option II already years ago but have not been able to decide.
About second quantization of the induced spinor fields The anticommutation relations for the induced spinors have been a longstanding issue and during years I have considered several options. The solution of the problem looks however stupifuingly simple. The conserved fermion currents are accompanied by supercurrents obtained by replacing Ψ with a mode of the induced spinor field to get u_{n}Γ^{α}Ψ or ΨΓ^{α}u_{n} with the conjugate of the mode. One obtains infinite number of conserved super currents. One can also replace both Ψ and Ψ in this manner to get purely bosonic conserved currents Ψ_{m}Γ^{α}u_{n} to which one can assign a conserved bosonic charges Q_{mn}. I noticed this years ago but did not realize that these bosonic charges define naturally anticommutators of fermionic creation and annihilation operators! The ordinary anticommutators of quantum field theory follow as a special case! By a suitable unitary transformation of the spinor basis one can diagonalize the hermitian matrix defined by Q_{mn} and by performing suitable scalings one can transform anticommutation relations to the standard form. An interesting question is whether the diagonalization is needed, and whether the deviation of the diagonal elements from unity could have some meaning and possibly relate to the hierarchy h_{eff}=n× h of Planck constants  probably not. Is statistical entanglement "real" entanglement? The question about the "reality" of statistical entanglement has bothered me for years. This entanglement is maximal and it cannot be reduced by measurement so that one can argue that it is not "real". Quite recently I learned that there has been a longstanding debate about the statistical entanglement and that the issue still remains unresolved. The idea that all electrons of the Universe are maximally entangled looks crazy. TGD provides several variants for solutions of this problem. It could be that only the fermionic oscillator operators at partonic 2surfaces associated with the spacetime surface (or its connected component) inside given CD anticommute and the fermions are thus indistinguishable. The extremist option is that the fermionic oscillator operators belonging to a network of partonic 2surfaces connected by string world sheets anticommute: only the oscillator operators assignable to the same scattering diagram would anticommute. What about QCC in the case of entanglement. EREPR correspondence introduced by Maldacena and Susskind for 4 years ago proposes that blackholes (maybe even elementary particles) are connected by wormholes. In TGD the analogous statement emerged for more than decade ago  magnetic flux tubes take the role of wormholes in TGD. Magnetic flux tubes were assumed to be accompanied by string world sheets. I did not consider the question whether string world sheets are always accompanied by flux tubes. What could be the criterion for entanglement to be "real"? "Reality" of entanglement demands some spacetime correlate. Could the presence of the flux tubes make the entanglement "real"? If statistical entanglement is accompanied by string connections without magnetic flux tubes, it would not be "real": only the presence of flux tubes would make it "real". Or is the presence of strings enough to make the statistical entanglement "real". In both cases the fermions associated with disjoint spacetime surfaces or with disjoint CDs would not be indistinguishable. This looks rather sensible. The spacetime correlate for the reduction of entanglement would be the splitting of a flux tube and fermionic strings inside it. The fermionic strings associated with flux tubes carrying monopole flux are closed and the return flux comes back along parallel spacetime sheet. Also fermionic string has similar structure. Reconnection of this flux tube with shape of very long flattened square splitting it to two pieces would be the correlate for the state function reduction reducing the entanglement with other fermions and would indeed decouple the fermion from the network. See the chapter Number Theoretical Vision.
