Abstract

This chapter represents the most recent (2014) view about particle massivation in TGD framework. This topic is necessarily quite extended since many several notions and new mathematics is involved. Therefore the calculation of particle masses involves five chapters. In this chapter my goal is to provide an up-todate summary whereas the chapters are unavoidably a story about evolution of ideas.

The identifcation of the spectrum of light particles reduces to two tasks: the construction of massless states and the identification of the states which remain light in p-adic thermodynamics. The latter task is relatively straightforward. The thorough understanding of the massless spectrum requires however a real understanding of quantum TGD. It would be also highly desirable to understand why p-adic thermodynamics combined with p-adic length scale hypothesis works. A lot of progress has taken place in these respects during last years.

1. Physical states as representations of super-symplectic and Super Kac- Moody algebras.

The basic constraint is that the super-conformal algebra involved must have ve tensor factors. The precise identication of the Kac-Moody type algebra has however turned out to be a dicult task. The recent view is as follows. Electroweak algebra U(2)ew = SU(2)L U(1) and symplectic isometries of light-cone boundary (SU(2)rot SU(3)c) give 2+2 factors and full supersymplectic algebra involving only covariantly constant right-handed neutrino mode would give 1 factor. This algebra could be associated with the 2-D surfaces X2 defined by the intersections of light-like 3-surfaces with δM4± CP2. These 2-surfaces have interpretation as partons.....