What's new inTGD: Physics as InfiniteDimensional GeometryNote: Newest contributions are at the top! 
Year 2014 
Higgs and padic mass calculationsIn the earlier blog posting I told that the boundary condition for the KählerDirac equation is massless Dirac equation with the analog of Higgs term added. The interpretation in terms of Higgs mechanism however fails since the term can be also tachyonic. Intriguingly, padic mass calculations require the ground state conformal weight to be negative half odd integer. This raises the question whether the the boundary condition for KählerDirac equation could be equivalent for the mass formulation given by the condition that the scaling generator L_{0} annihilates the physical states for Super Virasoro representations. This equivalence is suggested by quantum classical correspondence. If this is the case, the two mass shell conditions would be equivalent. This possibility is discussed more precisely below.

Welldefinedness of the em charge is the fundamental on spinor modes. Physical intuition suggests that also classical Z^{0} field should vanish  at least in scales longer than weak scale. Above the condition guaranteeing vanishing of em charge has been discussed at very general level. It has however turned out that one can understand situation by simply posing the simplest condition that one can imagine: the vanishing of classical W and possibly also Z^{0} fields inducing mixing of different charge states.
R_{01}= e^{0} ∧ e^{1}e^{2}∧ e^{3} , R_{23}= e^{0}∧ e^{1} e^{2}∧ e^{3} ,
R_{02}=e^{0}∧ e^{2}e^{3} ∧ e^{1} , R_{31} = e^{0}∧ e^{2}+e^{3}∧ e^{1} ,
R_{03} = 4e^{0}∧ e^{3}+2e^{1}∧ e^{2} , R_{12 = 2e0∧ e3+4e1∧ e2 . }
R_{01}=R_{23} and R_{03}= R_{31} combine to form purely left handed classical W boson fields and Z^{0} field corresponds to Z^{0}=2R_{03}.
Kähler form is given by
J= 2(e^{0}∧e^{3}+e^{1}∧ e^{2}) .
e^{0}∧ e^{1}e^{2}∧e^{3} =0 ,
e^{0}∧ e^{2}e^{3} ∧e^{1} ,
4e^{0}∧ e^{3}+2e^{1}∧e^{2} .
Also classical Z^{0} vanishes if a^{2}= 2 holds true. This guarantees that the couplings of induced gauge potential are purely vectorial. One can consider other alternaties. For instance, one could require that only classical Z^{0} field or induced Kähler form is nonvanishing and deduce similar condition.
See the chapter The recent vision about preferred extremals and solutions of the modified Dirac equation or the article.
Class field theory and TGD: does TGD reduce to number theory?The intriguing general result of class field theory) something extremely abstract for physicist's brain  is that the the maximal Abelian extension for rationals is homomorphic with the multiplicative group of ideles. This correspondence plays a key role in Langlands correspondence (see this,this, this, and this). Does this mean that it is not absolutely necessary to introduce padic numbers? This is actually not so. The Galois group of the maximal abelian extension is rather complex objects (absolute Galois group, AGG, defines as the Galois group of algebraic numbers is even more complex!). The ring Z of adeles defining the group of ideles as its invertible elements homeomorphic to the Galois group of maximal Abelian extension is profinite group. This means that it is totally disconnected space as also padic integers and numbers are. What is intriguing that pdic integers are however a continuous structure in the sense that differential calculus is possible. A concrete example is provided by 2adic units consisting of bit sequences which can have literally infinite nonvanishing bits. This space is formally discrete but one can construct differential calculus since the situation is not democratic. The higher the pinary digit in the expansion is, the less significant it is, and padic norm approaching to zero expresses the reduction of the insignificance. 1. Could TGD based physics reduce to a representation theory for the Galois groups of quaternions and octonions? Number theoretical vision about TGD raises questions about whether adeles and ideles could be helpful in the formulation of TGD. I have already earlier considered the idea that quantum TGD could reduce to a representation theory of appropriate Galois groups. I proceed to make questions.
2. Adelic variant of spacetime dynamics and spinorial dynamics? As an innocent novice I can continue to pose stupid questions. Now about adelic variant of the spacetime dynamics based on the generalization of Kähler action discussed already earlier but without mentioning adeles (see this).
3. Objections The basic idea is that appropriately defined invertible quaternionic/octonionic adeles can be regarded as elements of Galois group assignable to quaternions/octonions. The best manner to proceed is to invent objections against this idea.
See the new chapter Unified Number Theoretical Vision or the article with the same title. 
General ideas about octonions, quaternions, and twistorsOctonions, quaternions, quaternionic spacetime surfaces, octonionic spinors and twistors and twistor spaces are highly relevant for quantum TGD. In the following some general observations distilled during years are summarized. There is a beautiful pattern present suggesting that H=M^{4}× CP_{2} is completely unique on number theoretical grounds. Consider only the following facts. M^{4} and CP_{2} are the unique 4D spaces allowing twistor space with Kähler structure. M^{8}H duality allows to deduce M^{4}× CP_{2} via number theoretical compactification. Octonionic projective space OP_{2} appears as octonionic twistor space (there are no higherdimensional octonionic projective spaces). Octotwistors generalise the twistorial construction from M^{4} to M^{8} and octonionic gamma matrices make sense also for H with quaternionicity condition reducing OP_{2 to to the twistor space of H. } A further fascinating structure related to octotwistors is the nonassociated analog of Lie group defined by automorphisms by octonionic imaginary units: this group is topologically sixsphere. Also the analogy of quaternionicity of preferred extremals in TGD with the Majorana condition central in super string models is very thought provoking. All this suggests that associativity indeed could define basic dynamical principle of TGD. See the new chapter Unified Number Theoretical Vision or the article. 
Recent View about Kähler Geometry and Spin Structure of "World of Classical Worlds"?The construction of Kähler geometry of WCW ("world of classical worlds") is fundamental to TGD program. I ended up with the idea about physics as WCW geometry around 1985 and made a breakthrough around 1990, when I realized that Kähler function for WCW could correspond to Kähler action for its preferred extremals defining the analogs of Bohr orbits so that classical theory with Bohr rules would become an exact part of quantum theory and path integral would be replaced with genuine integral over WCW. The motivating construction was that for loop spaces leading to a unique Kähler geometry. The geometry for the space of 3D objects is even more complex than that for loops and the vision still is that the geometry of WCW is unique from the mere existence of Riemann connection. The basic idea is that WCW is union of symmetric spaces G/H labelled by zero modes which do not contribute to the WCW metric. There have been many open questions and it seems the details of the earlier approach must be modified at the level of detailed identifications and interpretations. What is satisfying that the overall coherence of the picture has increased dramatically and connections with string model and applications of TGD as WCW geometry to particle physics are now very concrete.
