As part of our ongoing service to the quantum information community, we here at the Quantum Pontiff would be remiss if we didn’t remind you of important upcoming deadlines. We all know that there is a certain event coming in February of 2014, and that we had better prepare for it; the submission deadline is fast approaching.
Therefore, let me take the opportunity to remind you that the deadline to submit to the special issue of the journal Symmetry called “Physics based on two-by-two matrices” is 28 February 2014.
Articles based on two-by-two matrices are invited. … It is generally assumed that the mathematics of this two-by-two matrix is well known. Get the eigenvalues by solving a quadratic equation, and then diagonalize the matrix by a rotation. This is not always possible. First of all, there are two-by-two matrixes that cannot be diagonalized. For some instances, the rotation alone is not enough for us to diagonalize the matrix. It is thus possible to gain a new insight to physics while dealing with these mathematical problems.
I, for one, am really looking forward to this special issue. And lucky for us, it will be open access, with an article processing charge of only 500 Swiss Francs. That’s just 125 CHF per entry of the matrix! Maybe we’ll gain deep new insights about such old classics as $latex \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$, or tackle the troublesome and non-normal beast, $latex \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}$. Who knows? Please put any rumors you have about great new 2×2 matrix results in the comments.
Sidney Coleman liked to tease Shelly Glashow by saying that Shelly had won a Nobel Prize using no more mathematical knowledge than how to diagonalize a 2 X 2 matrix. In fact, Glashow did some amazing physics with 2 X 2 matrices, including his 1961 paper on the SU(2) X U(1) model and his 1970 paper with Iliopoulos and Maiani on charm.
I just checked Google scholar: the 1961 paper has 6287 citations and the 1970 paper has 4978 citations. A lot of citations per matrix entry.
John, this is amazing.
It also raises the important question: which theory paper has the highest number of citations per matrix entry? Immediately ruled out are any asymptotic results, which means that only very few papers will be left. Looking at an obvious candidate, the teleportation paper of my co-blogger Charlie Bennett et al., it has roughly 10k citations. It does include some asymptotic extensions, but the main result is using pure states of at most 3 qubits. A harsh interpretation of the rules (10k / 64 = 150) would mean that the GIM paper trounces the teleportation paper! Bell’s 1964 paper (8k / 16 = 500) does much better, but still loses badly. Are there any other contenders?
Perhaps a better metric is the number of citations divided by the log of the size of the matrix.
Presumably this will be followed by another special issue, on 3 by 3 matrices. Much more complicated!
I will divide up my next paper on n-by-n matrices into one paper for each of the journals in this series, and cite each of my previous papers.
That would be funny, except that it is an actual research strategy for some people. [e.g., El Naschie 😉 ]
Kobayashi and Maskawa became famous by generalizing what Glashow-Iliopoulos-Maini did (a two-by-two matrix describing the misalignment between quark mass eigenstates and weak interaction eigenstates for two generations) to three generations. That was a three-by-three matrix and was indeed more complicated. GIM’s matrix explained the Cabibbo angle, and KM generalized that to three angles and a (CP-violating) phase. The paper is famous because it explained the origin of CP violation in the standard model.
8837 citations on Google Scholar as of today, and another Nobel Prize.
Just for the record, Glashow’s two-by-two matrix in 1961 was also relevant to the standard model — he diagonalized the mass matrix of the photon and Z-boson. He, too, explained an important angle, which we now call the Weinberg angle.
Heck, some mathematicians spend their entire careers studying 1 by 1 matrices.
My original paper on quantum games, subsequently published in PRL, was rejected by Science with the comment that it was too mathematical—presumably because it used 2×2 density matrices.