A story about the Solari-Kochetov phase

Not too long ago I was applying for promotion to the CONICET (Argentine National Science Council). I had to do a good deal of paperwork for the presentation, this paperwork included certainly the list of publications and their citations. I asked a friend with access to the SCI-citation index to find them for me.

The popularity of my works (the citation index measures a social property of our work) was as expected. No surprises at all except for one paper. A 1987 paper I wrote after completing my PhD and before starting my postdoctoral position had increased the citation number from one (1) isolated cite in 1993 to more than ten (10) by 2002 (more than 29 by 2012).

I've got curious about what could have happened to a this completely forgotten paper?. Actually, I liked the paper, it was the last paper in a short series of two, coming from the time when I was trying to obtain a semiclassical quantisation formulae using coherent states, highly influenced by Gutzwiller works as well as Gilmore-Perelomov coherent states. As soon as I began working in the subject, I realized that I would have to get the semiclassical-time-propagator in terms of coherent states in proper form since it was utterly clear that there were problems with it. Actually, Schulman had already pointed to the problems in his book on Path Integrals.

By 1987 I had two independent forms of getting the propagator, one in terms of the inner representation of coherent states ad the other in terms of the outer representation , both expressions were obtained by substantially different methods, they were in agreement and gave the correct result in the trivial tests cases (i.e., they survived the meta-conceptual tests that previous attempts have failed). I was about to learn a lesson a would not forget: science is a social endeavor governed by social rules. The social consensus had established that the obviously incorrect results were correct, exception made of the anonymous referee that wrote "this manuscript is very poorly written but unfortunately,, it is correct". In part because nobody gave credit to my work, I decided to move away from the field and landed in Nonlinear Dynamics for my own good.

Back to the story. What and when something had happened for a forgotten paper to be rescued? I pursued the question as an entertainment browsing the WeB (naturally). I soon came across the "Solari Kochetov phase" and finally I learned about the work by M. Stone, Kee-Su Park and A. Garg (The semiclassical propagator for spin coherent states. Journal of Mathematical Physics 41, 8025-8049 (2000)), that I believe, coined the expression "Solari Kochetov phase".

It turns to be that Kochetov had rediscovered independently the proper form of the semiclassical evolution operator for spin systems in 1995, actually, there was at least one more independent rediscovery (Vieira-Sacramento 1995); these works apparently suffered the same fate than mine.

But the semiclassical-propagator is a tool, and the real test for a tool is to use it. The semiclassical propagator appeared to be useful for computations of Spin-tunnelling, but researchers found it to be unreliable and turned to other methods after being deceived by the socially accepted versions of the early 80's. Stone, Park and Garg are to be credited for bringing into focus the several times found (and forgotten) correction.

Some times I am asked, why is chaos so important? what is all this excitation about chaos? I like to give the social reason: chaos was known to Poincaré, Birkhoff and others, actually, von Newmann used the word chaos referring to the dynamics close to Poincaré's homoclinic orbits; but this kind of dynamics was largely forgotten by the scientific community and (almost?) erased from textbooks. The social excitation of the rediscovering is just proportional to the neglect!

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