All the papers I mention below can be found on Google Scholar by the keyword “Alexander Migdal”.
I started very early, as an undergraduate student in FizTech. I am quite proud of my second paper, where we discovered with my best friend Sasha Polyakov dynamical mechanism of symmetry breaking and mass generation in Gauge Theory in 1964, independently of Higgs, Englert and Brout. Conservative Landau School fiercely fought against us, so that our paper got rejected twice in JETP and was finally published only in 1966. Being so delayed we cannot claim credit for this discovery, but we can be satisfied that we stood against retrogrades and fought for the truth we discovered.
Next notable paper was my work with Vladimir Gribov in 1967-68 where we discovered anomalous dimensions in scale invariant field theory. I later applied this, parallel with similar work by Sasha Polyakov- to the critical phenomena in statistical physics. Our pass was taken by Kenneth Wilson, who scored goal of quantitative theory of phase transitions, applying the renormalization group and his famous expansion.
I worked with Gribov for a few years in his Reggeon Field Theory, which was technicaly quite advanced but became obsolete after discovery of Asymptotic Freedom by Gross, Wilczek and Politzer. I left everything and dove into QCD- The Theory of Strong Interactions.
I discovered quark-resonance duality which led to QCD sum rules of Shifman Wainshtein and Zakharov. I was still working on this theory just two years ago, bringing together the ideas of CFT and String theory, explaining some mysterious relations between my phenomenological QCD spectrum from the 70-ties and remarkable AdS-CFT analogy discovered in the last decades. Remarkably, my phenomenological formulas, relating the string mass spectrum to the spectrum of dimensions of CFT as roots and indexes of Bessel functions were rediscovered 30 years later in the context of the AdS-CFT duality.
I worked many years in the field of Large N QCD and Quantum Gravity, establishing analogy between QCD and String theory. I have some notable achievements such as Loop Equation in Large N QCD (which reduced field theory to nonlinear 1D problem of loop dynamics).
Another work, which created some excitement in academic community was exact solution of 2D Quantum Gravity, which was started in series of my papers with Volodya Kazakov and was finished with help from David Gross, Edouard Brezin and Shenker and Douglas.
Since that time, in the 90’s my work was mostly some technical advances such as Loop Equations in Turbulence, where I reduced 3D field theory of decaying turbulence to nonlinear stochastic 1D ODE. This equation can be used to solve large dimension limit of Turbulence (dimension enters as a parameter rather than number of degrees of freedom). Alas, I never finished that work.
Neither did I finish my work on algebraic formulation of the QCD momentum loop equation. Again, it opened the way to exact solution in the infrared limit, which I never found.
Wind of Fate was already blowing and I could not resist its pull. I started new life in the Industry, as an Inventor and Entrepreneur. I opened Internet start-up in mid-90’s with couple of students. A year later I sold the company to the public company and left Academia for good. It was a stressful life, but I never regretted quitting my beloved Princeton University.
Through my academic career I mostly generated ideas, but in my industrial career I had to develop and implement my ideas into working products and technologies. These technologies made it to Windows 98, AOL7, Minolta 3D camera, Lockheed-Martin RealScan3D and other products. I founded a public company and have served as Vice Chairman and Chief Scientist of this Company (VWPT) until March 2000, when I left it to work on stock trading system. This is what I still do today, with intermittent success, but unwavering enthusiasm.