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.....
Keywords: Massless particles, particle massivation, hadron massivation, mass
formula, p-adic numbers, p-adic physics, p-adic thermodynamics,
canonical identi cation, superconformal invariance, supersymplectic
algebra, partition function, Super-Kac-Moody algebra, Super-
Virasoro algebra, Yangian algebra, modular invariance, genus, family
replication phenomenon, CKM mixing, topological mixing, Higgs.
