-IMHO top quark will not earn a nobel, but of course this is arguable but it was totally expected, its big mass was anticipated from ARGUS results (more on that later…), anyway lets say it is nobel worthy, what amazes me is that nobody mentions the direct detection of the tau neutrino by the DONUT experiment in 2000 which was also totally expected… bla bla… my point is if top detection deserves a nobel so does tau neutrino.
-Of course the CKM trio deserves a nobel, they really deserved it for a long time and its just a little taste of how outrageous this kind of decisions can be, for example why Chien-Shiung Wu didn’t received it and the list can go on (Edwin Hubble, Zeldovich, Stueckelberg…).
-Why doesn’t anyone menctions DESY !?! Some of Europes biggest achievements were realized there, gluons were discovered there (now, that’s nobel-worthy), B mesons oscillations were discovered also at DESY (which opened the field for so many collaborations like Hera-b, Babar, Belle, LHCb…). And talking about “fiascos”, HERA was filled with lots of expectations (and in 1997 caused such a big stir with the leptoquark issue) and seemed to came out with empty hands, although at least their prediction measurements of qcd (specially deep inelastic scattering) contributed to the nobel to asymptotic freedom trio.

The transformation properties of the field, of which the quanta are excitations, specify the essential properties of the particles: mass, spin (spacetime properities), statistics (fermion, boson), and a host of internal quantum numbers according to the symmetries the field is assumed to have. The particle nature of these quanta is somewhat straightforward but also uninteresting if the field is free (non-interacting). If the field interacts, with itself or with other fields, the picture gets quite complicated.

In the perturbative approach to studying interactions Feynman introduced a nice computational device that allows one to write down the terms of the perturbation expansion with a graphic shorthand notation rather than the complex (hard to remember) field-theoretic symbols. The free-field current (a free quantum) is dipicted as a line. Interacting currents, at coarsest perturbation level, are represented as two asymptotically free currents that interact by exchanging another type of line, a propagator of the interaction field, that correlates the two currents. The concept of “virtual particles” is used to describe this line but these “particles” are far less particles than the free-particles and create all kinds of conceptual problems for non-propfessional amateurs.

All three gauge bosons acquire a mass, no unbroken U(1) survives. To get an unbroken U(1), you need to step up to the vector representation, which gives you two massive charged gauge bosons and an uncharged massless one.

Sorry about that. I need an edit button. Or more coffee and fewer distractions. Or all of the above.

P.S. Try a creation operator acting on the vacuum.

As for creation operators, I suggest other blogs might be a better place to discuss them

Cheers,
T.

Then is a square root of a creation operator half a particle?

Hi BEGINNER.
For beginners here is what I still remember Weinberg wrote 20 years ago: More or less he wrote that a particle is a representation of its symmetry group(s). Once you said how a particle behaves repect to symmetry transformations (translations, rotations, labeling, gauge,…) then you’ve said everything you can about that particle.

The hot, updated and professional theoretical contributors to the forum will certainly orrect me or set me straight. Lets see that they say. Remember that particles are “just” (*) excitations of fields.

jeff

(*) BEGINNER. Try asking a theoretical physicst to explain how a field excitation can leave a track of ionization in a detector. If the field (2nd quantization) context is too abstract for you then ask him how he would explain a quantum mechanical particle/wave can leave a nice track.

Seriously, you are simplifying a bit too much here. If you have a Higgs in the fundamental representation of SU(2), it breaks the symmetry completely. All three massive gauge bosons acquire a mass, no unbroken U(1) survives. To get an unbroken U(1), you need to step up to the vector representation, which gives you two massive charged gauge bosons and an uncharged one. Georgi and Glashow tried that one, but without a Z, it’s now a historic curiosity.

The real reason that the U(1) of hypercharge mixes with one of the U(1) subgroups of SU(2)_L is that the Higgs is engineered to get that result, by carrying both hypercharge and and weak isospin charge. So it breaks both, but since there are only three independent Higgs components (fixing the VEV eliminates one degree of freedom) and four gauge fields, a linear combination of the latter remains massless.

Nige, I think what you are getting at is something which probably crosses the mind of everybody who starts pondering the structure of electroweak interactions. I think it’s even a pet puzzle of Not Even Woit.

Basically, you are thinking that the Lorentz group is SU(2)_LxSU(2)_R, the electroweak group is SU(2)_LxU(1), and it really looks like one ought to be able to find a deeper underlying explanation for this similarity. Like maybe get the U(1) of hypercharge by breaking an SU(2)_R with a Higgs in the vector representation, a la Georgi and Glashow, and then let the two massive R gauge bosons form a spin 2 bound state, to be identified with the graviton. Make the SU(2)_R symmetry breaking scale low enough (the dark energy scale, eh?) and this “graviton” might be almost exactly massless, while enough confinement might survive to explain why you never see the two charged gauged bosons in isolation. Who knows, you might even be able to get the right running to explain the rotation curves of galaxies.

As you probably guessed, I’m being a little facetious here. In words, it all sounds very easy. The devil is in the details. You could start with the equivalence principle: how would you make this “gravity” act equally on all kinds of matter, independently of composition, and bend light as observed? Remember, most mass around us is not due to the Yukawa couplings between Higgs and fermions. Some 99%+ of it is the energy of quarks and gluons bound together and furiously running around inside hadrons. How exactly would your gravity couple to that, and how would it couple to light, all in a manner that reproduces the experimentally verified predictions of general relativity?

Work that one out, and fame (but probably not riches) will be yours.

Regarding your other point, it is highly unlikely that gravitational interactions have anything whatsoever to do with the Weinberg angle.

Kea, comment 10: people haven’t tried to find a lagrangian for massless SU(2) gauge bosons interactions where the massless neutral current is quantum gravity and the massless charged currents mediate electromagnetic interactions. The nearest thing was the 1957 incorrect Schwinger-Glashow theory in which the massless neutral current of SU(2) was used to replace U(1) for electromagnetism, and the two charged field quanta of SU(2) were used for weak interactions. This is not what I’m arguing which is that the two charged massless field quanta of SU(2) are electromagnetic field quanta (the extra polarizations of the virtual photon are electric charge) and the massless neutral field quantum is the graviton.

If there is a way of using noncommutative geometry to deal with Feynman diagrams in place of have a path integral with involving an amplitude containing an action which is an integral of a lagrangian equation for the gauge theory, then please let me know. I’m interested in path integrals because for low-energy approximations (representing the Newtonian and Coulomb laws), the only significant contribution to the interaction histories summation is for the simplest Feynman diagram, i.e., a simple exchange of a photon between charges. All of the loop diagrams can be ignored at low energy for the classical approximations. So the only summing of histories in the path integral is for that single simple type of interaction integrated over all possible paths in spacetime, each with an equal contribution but a different phase vector that determines interference. The first priority is to check how this theory works for low-energy physics.

Tony Smith, comment 13: thanks for that information that you have the Weinberg mixing angle calculated from your model, pages 82-86 in http://www.tony5m17h.net/E8physicsbook.pdf Your physics writings are always fascinating. Your calculation of the Weinberg mixing angle on page 85, namely Sin(theta_w)^2 = 1 – (M_W+/- / M_Z0)^2 = 1 – ( 6452.2663 / 8438.6270 ) = 0.235, is impressive. I don’t however physically understand how the B gauge boson of U(1) gets mixed with that of the neutral W_0 boson of SU(2) to produce the observed photon and the observed weak boson Z_0. Mixing of gauge bosons would physically make more sense to me if it was between massless and massive versions of gauge bosons within the same symmetry group such as SU(2), i.e., mixing of massive and massless versions of the SU(2) gauge bosons might occur with a physical mechanism in terms of how the Higgs-type field gives mass to SU(2) gauge bosons as a function of handedness and energy.

Eric, comment 14: ‘Quantum mechanically, two U(1)’s generically are going to mix together whether you like it or not.’ The mixing is between the gauge boson of one U(1) and the neutral gauge boson of SU(2). It’s not the U(1) weak hypercharge gauge boson B and the U(1) electromagnetic photon which are being mixed together to produce the W_0 and the Z_0. It’s instead the weak hypercharge U(1) unobserved gauge boson, ‘B’, and the SU(2) unobserved W_0 get mixed up to produce the two observables, the photon and the Z_0.

‘In the SM, the Weinberg angle may seem ad hoc in the sense that it is a free parameter. However, the value of the Weinberg angle comes out automatically when one goes to SUSY GUTs.’

Thanks for this news, which is a competitor with Tony Smith’s calculation, but SU(5) GUTs, whether SUSY or not, don’t include gravity. Gravity and electromagnetism have similarities in both being long range interactions, needs to be incorporated into a a symmetry group.

A detailed account of it can be found in the book “The Evidence for the Top Quark” by Kent W. Staley (Cambridge 2004), particularly his chapter 1 entitled “Origins of the Third Generation of Matter”. It indicates to me that the work of Kobayahsi and Maskawa was quite brilliant (even if embedded in political controversy about Japan, the Nagoya group, and dialectical materialism).

As to Wheeler’s lack of a Nobel, the story is not as simple as “no experimentally confirmed prediction”. The whole story has not been published as far as I know, but I will start with Kip Thorne saying in his book “Black Holes and Time Warps”:
“… in 1958 … there arrived in Moscow an issue of the Physical Review with an article by David Finkelstein … Landau … read the article … It was a revelation … Finkelstein’s insight and the bomb code simulations fully convinced Wheeler that the implosion of a massive star must produce a black hole …”.

IIRC:
There was a push (backed by Princeton, Cambridge, etc) to get a Nobel prize for Wheeler based on his Black Hole idea,
but
Landau had a seat on the Nobel committee and black-balled Wheeler using the grounds that Finkelstein had priority.
However, Landau had a further reason to block Wheeler:
The Soviets felt that the Black Hole basis for the Princeton-Cambridge push for a Nobel for Wheeler was a sham, and that their real basis was to give Wheeler a Nobel for his bomb code work (which obviously had an abundance of “experimentally confirmed prediction”)
and the Soviets felt that if a Nobel were to go for bomb code work then Sakharov should also get a Nobel for his bomb code work.
However,
the Nobel committee did not want to give prizes for war-weapons work, so a joint Wheeler-Sakharov bomb code prize would not happen,
so
the Soviets, through Landau’s black-ball, made sure that a Nobel would not go to Wheeler without Sakharov.

Human politics is interesting, but sort of sad.

Tony Smith

In hindsight I find it hard to judge how brilliant the CKM construct was. From a mathematical point of view it’s a simple example of singular value decomposition, which was completely worked out for the general complex case sometime in the 30s. Once you realize that you have multiple generations and that nothing prevents them from mixing, it’s unavoidable. Not sure why you say it was central to making the top completely expected; I would say that followed from anomaly cancellation, which happens in group space, no need to consider mass eigenstate mixing. Am I missing something?

I think I can answer why Wheeler never got the prize: no experimentally confirmed prediction. Seems to be an unwritten rule of the Nobel committee that only such theoretical work is eligible.

sorry for letting this thread grow without contributing. A few things.

1) MM, the Michelson-Morley experiment was little more than a table-top experiment, it could only have two outcomes, and both were interesting. I would not compare it to four giant detectors running for years, 2000+ physicists, O(1 billion dollars) investment, who went head down for the Higgs, and argued endlessly that they should continue running on the basis of a 1.7-sigma excess at 115 GeV (which they presented as more than 3-sigma back then!).

2) GW, Eric, I think you do not need my input… I am happy that you clarified the matter however.

3) DB, the W and Z discovery earned Van der Meer a nobel prize -quite right also according to your metric, since it was a breakthrough in the technology necessary to advance the field- but it won Rubbia another. Now, W and Z bosons were not only known to exist well before 1983 (after 1978 nobody in the field believed they did not exist), but their mass was also quite well known beforehand, with the clear implications for the possibility to “tune” the experiment in their search.
The top quark was thought to exist by most, but was not just as much called for. Sure, after the measurement of I_3^b by LEP nobody doubted. But the mass could be anywhere between 100 and 200 GeV by 1992. So I think that discovery deserves a nobel prize at least as much as Rubbia’s one did.

Cheers,
T.

2)

If you take DB’s position, and you realize that what made the T-quark “completely expected” was the success of the Kobayashi-Maskawa 3-generation mixing matrix,
you would think that Kobayashi and Maskawa would have won a Nobel for brilliant theoretical work confirmed by experiment.

Why do you think that they are not Nobel laureates?

Tony Smith

PS – Further, weren’t Nobel prizes given for both theoretical models AND subsequent experimental discovery of the then-completely-expected W-bosons?

The Higgs particle is another matter. It is by no means obvious or certain that it must exist.

And supersymmetry is another matter again. It’s always just around the corner, and has been for 35 years. Now the the next corner is about to be turned we’re hearing a lot about split supersymmettry, which is designed to save string theory in case the LHC doesn’t find supersymmetry.

Regarding SUSY or non-SUSY, I don’t think that the statement that the former work better in this respect is meaningful in isolation. You can always tune a running value to fit low energy measurements e.g. by moving the GUT scale. Maybe you are thinking of the convergence of the couplings? That certainly works better in simple SUSY GUTs than in non-SUSY ones, and can reasonably be considered a hint in favor of SUSY.