The physical information lies in the relative signs...
By unifying quarks and leptons into a single class, the most important properties of these particles can be summarized in a set of rules for dealing with symmetrical symbols. The appropriate mathematical structure (the 16- dimensional spinor representation of SO(10)) is formidable, but some appreciation of the scheme can be conveyed fairly simply.
The core of the Standard Model is the idea that the non-gravitational interactions of matter, the strong, weak and electromagnetic interactions, are all described by the responses of particles called gauge bosons (the photon, for example) to several types of charge. These charges are usually called ‘colours’. The gauge bosons of the strong interaction respond to and change three colours, usually called red, white and blue. The gauge bosons of the weak interaction respond to and change two colours, let us call them green and purple. The remaining ‘hypercharge’ gauge boson, from which the ordinary photon is constructed, responds to a combination of charges: one-half the sum of green and purple, minus one-third the sum of red, white and blue. The Standard Model does not explain why this particular combination is picked out, but it is inevitable within unification schemes such as SO(10).
This follows from one of the formal rules, the ‘bleaching rule’, that an equal mixture of all available charges cancels out. Thus, for example, a particle carrying a unit of red plus a unit of white colour charge will look the same, as far as the colour gluons of the strong interaction are concerned, as if it carried a negative unit of blue charge: the sum of red, white and blue units cancels.
The bleaching rule eliminates from the strong interaction the gauge boson that responds to the sum of red, white and blue charges, and from the weak interaction the gauge boson that responds to the sum of green and purple charges. These are bogus particles: ‘gauge bogons’. Likewise, it eliminates from the unified model, which treats all five colours together, the gauge boson that couples to the sum of all five colours. However, the difference between total weak and strong colour charges is not bleached out. The gauge boson that responds to this (the difference between the strong and weak gauge bogons) is precisely the hypercharge component of the Standard Model.
The multiplet shown here is constructed as a five-bit register, with entries + and −, subject to the rule that the total number of − signs is odd (in each case, changing all the signs gives the right-handed particle equivalent, not shown). Each entry corresponds to either plus or minus half a unit of the associated colour charge. So the first particle has half a unit each of green and purple charge; these cancel according to the bleaching rule, so this particle has no weak interaction. It has minus half a unit of red charge, and half a unit each of white and blue charge, equivalent to minus a full unit of red charge. These are precisely the properties of one of the particles in nature: the antiparticle of the righthanded red down quark. In all the rows up to the last, we find a precise match between the mathematical demands of this scheme and observed particles.
But the last row describes a totally bleached particle. It has neither strong, nor weak, nor electromagnetic interactions. It is none other than our new friend, the particle that according to this scheme gives mass to the neutrino: the N.
The Standard Model transcended, Frank Wilczek
... in the asymptotic expansion of a spectral action functional
I was asked to referee the Chamseddine-Connes paper which they submitted to a physics magazine in a attempt to break out of the noncommutative club. My enthusiastic recommendation - competent to the extent that I had just independently checked the action computation - was willingly ignored by the editor of the magazine who rejected a "paper without experimental confirmations" (in contrast with the rest of the mathematical physics literature, including the strings abounding in this magazine - and overseeing relative signs, as though stability of the world was no important experimental fact).
Noncommutative geometry and fundamental physical interactions: The Lagrangian level—Historical sketch and description of the present situation 2000Daniel Kastler
The arbitrary mass scale in the spectral action for the Dirac operator in the spectral action is made dynamical by introducing a dilaton field. We evaluate all the low-energy terms in the spectral action and determine the dilaton couplings. These results are applied to the spectral action of the noncommutative space defined by the standard model. We show that the effective action for all matter couplings is scale invariant, except for the dilaton kinetic term and Einstein-Hilbert term. The resulting action is almost identical to the one proposed for making the standard model scale invariant as well as the model for extended inflation and has the same low-energy limit as the Randall-Sundrum model. Remarkably, all desirable features with correct signs for the relevant terms are obtained uniquely and without any fine tuning
(last revised 16 Mar 2006 (this version, v3))
The crucial information (from the physical point of view) lies actually not in the exact values of the coefficients but their relative signs. If H2 and H4 appear with opposite signs we have the standard Higgs potential leading to the symmetry breaking mechanism.
Any vague resemblance to a recent issue dealt with by other bloggers is (not completely ;-) fortuitous.
//last edition 7 June 2015