Alexander Migdal made important contributions to the theory of critical phenomena, quantum chromodynamics and conformal field theory. As an undergraduate student he worked out the theory of the dynamical mass generation in gauge theories, commonly referred to as the "Higgs mechanism", in the spring of 1965, independently of Robert Brout, François Englert and Peter Higgs. In 1968 he published a paper which introduced scale invariance with anomalous dimensions to be determined as eigenvalues of bootstrap equations of quantum field theory. This work led to so called Migdal-Polyakov conformal bootstrap which had profound influence and helped to make progress in the theory of critical phenomena as well as the theory of strong interactions. In the next decade Migdal made important progress in quantum chromodynamics by introducing a novel form of the renormalization group, and by deriving the equation for the Wilson loops. The so-called Migdal program was a precursor and provided an impetus to the Shifman-Vainshtein-Zakharov sum rule method in QCD which presently plays a basic role in the calculations of hadronic properties. Later he found exact solution of quantum gravity in two dimensions, starting the topic of matrix models of topological field theories which occupied the physics community for a number of years. He also worked on the applications of quantum field theory to the theory of turbulence, and derived the exact loop equation for velocity circulation to describe this phenomenon. He initiated a description of intermittency in nonlinear systems by means of Instanton solutions of the stochastic differential equations. As of 2020, he is a research scientist at the New York University.
Entrepreneurship
Leaving Princeton tenure in 1996, he became an inventor and entrepreneur. He holds 10+ patents in laser scanning and 3D data compression/transmission, built first textured 3D scanner which was awarded as Best OfWhat's New and other industrial awards. He was director of several companies and invited speaker of numerous international conferences. Currently he is CEO of his fourth start-up company Migdal Research LLC dedicated to the stock market prediction.
