Many physicists believe that the Higgs boson is the last “elementary” particle which will be discovered. Many more physicists are patiently waiting for the discovery of a whole set of s-particles. Then, there is someone still believing that there is 4

^{th}generation of quarks and leptons. Of course, these questions will be answered by the LHC data one day, perhaps. Yet, can these questions be answered in this AP (Axiomatic Physics)? The answer is a big Yes. There are only 48 elementary particles exactly, no more or less.
In this AP, the space-time is not an egg-laying hen but is with a definite structure which is described with the equation below.

Delta S = N * C * (Delta T)

= (i^n1, i^n2, i^n3) * C * (Delta T) ..................... Equation zero

The n1, n2 and n3 can take the numbers {1, 2, 3 or 4}. That is, this N (trait matrix) describes a 64 state set (4 x 4 x 4 = 64). The inner-product (IP) of each this state can be of four values {+/- 1, +/- 3}.

That is, this inner product (IP) of N gives rise to two groups with two sub-groups each.

a. Positive (32 dimensions)

1. When IP = +1 (24 dimensions or states)

2. When IP = +3 (8 dimensions or states)

b. Negative (32 dimensions)

1. When IP = -1 (24 dimensions or states)

2. When IP = -3 (8 dimensions or states)

Why should n1, n2, and n3 take the numbers {1, 2, 3 or 4}? It is because that “time” has four dimensions in this AP, {+/- t, +/- it}.

Why are there three seats in N? I discussed this in my previous posts and will discuss it again soon. Yet, I will skip this question for now.

In “Prequark Chromodynamics, http://www.prequark.org/ “, on the rock bottom of this AP universe, there are two Prequark charges; [V (Vacutron), the vacuum] and [A (Angultron), an innate angle]. With these two charges and three seats, only four different kinds of states (or particles) can be formed, and I have given them the names of u- or d-quark and electron or neutrino. The fact that they have the same names as the known quarks and leptons is purely incidental.

When the seating arrangement is distinguishable for the four particles above, the two quarks above will become six distinguishable quarks (could be identified with three colors). Thus, the four states (or particles) above become 8 distinguishable states (or particles).

As there are 24 states when IP = +1, there can be three groups of states (or particles), as 24/8 = 3. When IP = 3, those states (8 of them) are not particles in this AP.

Thus, in this AP (Axiomatic Physics), the N (trait matrix) gives rise to the followings,

i. two rock bottom charges; V and A. Why, I will discuss this later.

ii. three seats (identified with three colors).

iii. 64 dimensions (states), a consequence of the “time” having 4 dimensions and the “space” having 3 seats.

iv. only 48 of the 64 states are particles. The other 16 states are a pure vacuum.

Now, in this AP, there are three groups of particles (the three generations). And, in each group, there are two types of particles (quarks or leptons). Then, each type has two flavors, such as, [(u- or d-quark) and (electron or neutrino)]. Of course, there is another set which is the anti-particles (when IP = -1), also with only 24 states (anti-particles). The above calculation is purely axiomatic in the framework of this AP while adding any “external elements” (not part of this axiom system) into the system is not allowed.

In conclusion, this AP (Axiomatic Physics) can accommodate “only” three generations of particles with two types of particles in each generation, and two flavors for each type of particle. Of course, there is an identical copy of the anti-particle universe. Thus, if any additional “fundamental” (not composite) particle (such as the Higgs boson, the 4

^{th}generation quarks or any s-particles) is discovery, then this AP must need to be amended. Before that, the issue of the origin of flavor and of generation is, now, answered.
In this AP, the force carries [photons, gluons and weak bosons (W and Z)] are not considered as the spacetime “structure” elementary particles. While the W and Z bosons are well-defined particles in an observational sense, they are only the transient states in this AP (see the article “Neutron Beta Decay, at http://www.prequark.org/Q2.htm “.

Furthermore, the numbers {64, 48 and 24} are the vital numbers for calculating many other “structure” parameters in this AP. And, we will see their appearances in many AP equations.

Note: the detail of the equation zero was discussed on the page 26 of the book “Super Unified Theory” (ISBN 0-916713-02-4, Copyright # TX 1-323-231, Library of Congress Catalog Card Number 84-90325). This book is available in many university libraries around the world, and that library info is available at the WorldCat (the world's largest library catalog).