I return in this brief Lab Note to the underlying spirit of one of the basic premises of this Weblog, which is that these are a series of “Lab Notes.” We often tend these days to think and speak about “theories,” rather than “notes,” and certainly, many of the “Lab Notes” which I am presenting here are intended to be thought of as “theories,” or “theories-under-development,” as much as “lab notes.”
But when one talks about “Lab Notes,” what should be the prevailing thought is that sometimes, in the course of research, one uncovers an interesting “data point.” Perhaps that data point goes nowhere; perhaps, when one looks hard at that data point and follows it up carefully, it leads in a whole new direction and changes many things in physics.
It is in this spirit that I present Lab Note 4, “An Interesting Left-Chiral Muliplet Perhaps Indicative of Preonic Structure for Fermions,” which I offer in the spirit of an interesting theoretical “data point” I uncovered back in 1988. No more, no less.
For some history, I had been auditing some physics courses at nearby Rensselaer Polytechnic Institute (which my daughter Paula is now attending as a Freshman Chemical Engineer), and in the course of my studies there began a dialogue and I later became friends with the tragically-late Professor Nimai Mukhopadhyay, who was a particle physicist.
At the time, particularly because of the “isospin redundancy” between quarks and leptons — which is my way of saying that both quarks and leptons can exist in both an “isospin up” and an “isospin down” state — I began to realize that there are really two distinct “attributes” which specify the “flavor” of an “elementary” fermion, within each generation. First: is it a “quark” or a “lepton”? Second, is its isospin “up” or “down.” And, this, I began to suspect, was indicative of a preon substructure for the fermions — part of which provided the quark versus lepton aspect of flavor, the other part of which provided the up versus down isospin aspect of flavor.
Following this thinking, I found that if one were to consider the flavor quantum numbers for only the left-chiral fermions, it turned out that the simple gauge group SU(4) could be used to represent the flavor symmetry of these left-chiral fermions, and that four preons, simply, A, B, C, D so as to avoid any preconceptions at all, could be used in pairs so as to construct the left-chiral fermion flavors. I wrote this up for the 1988 “Excited Baryons” conference at RPI, and Dr. Mukhopadhyay included the writeup with the conference program. For your consideration as a “lab note,” i.e., as an interesting piece of research data to keep in one’s mind, I link to a copy of that 1988 writeup below:
Left-Chiral Flavor Muliplet
At this point in time, 20 years later, it is clear to me that I am not the only person to have thought in this way. For example, G. Volovik, in his 2003 book “The Universe in a Helium Droplet,” includes an excellent discussion in section 12.2, which I have uploaded to the following link:
Volovik Excerpt on Quark and Lepton Preonic Structure
Volovik makes a separation very similar to what I was going after in 1988, does so very clearly, and also, nicely handles the right-chiral states which drove me to fits back in 1988. In fact, this excerpt from Volovik is another very important “lab note,” in and of itself, and I commend it to the reader. The main problem which I perceive with this excerpt from Volovik, however, is his handling of the spins, which motivates the use of “holons” (spin 0) and “spinons” (spin 1/2) to construct a spin 1/2 fermion out of two preons. In my view, it would be preferred for each of these preons to have spin 1/2, and when combined, for the resulting particle to also have spin 1/2. That is, we need to find a way to have 1/2 = 1/2 + 1/2.
How we do this is another story which utilizes the fact that a fermion is a four-component Dirac spinor, and that left- and right-chirality each occupy two of the four components. Thus, for the left- and right-chiral components of a fermion , each of which has spin 1/2, one can combine those into the whole four-component fermion — which still has spin 1/2. That is, may be a way to implement 1/2 = 1/2 + 1/2 within the context of Volovik, thereby avoiding the seemingly-artificial (to me) holons and spinons. But, that is a topic for another lab note, and this approach clearly exploits pre-existing chiral properties of fermions.
In any event, please take a look at my 1988 publication linked above, look also at the linked Volovik excerpt, think about his and my separation of the fermion flavor attributes into quark/lepton and isospin up/down, think about the inelegance of using holons and spinons (at least if you and I have the same sense of elegance), and think about the chiral properties of fermions. I do continue to believe the believe that the clearly-established “isospin redundancy” between quarks and leptons is the best evidence we have, of a preonic substructure for fermions which is waiting to be better understood, and cast into a suitable formal pedagogical structure.
That concludes this lab note.