# Alexander Arkadyevich Migdal

**Alexander Arkadyevich Migdal** (Russian: Александр Арка́дьевич Мигдал; born 22 July 1945) is a Russian – American physicist and entrepreneur, formerly at Landau Institute for Theoretical Physics, Space Research Institute, Princeton University, ViewPoint Corp, Magic Works LLC, and now at Migdal Research LLC.

Alexander Arkadyevich (Sasha) Migdal | |
---|---|

Born | |

Alma mater | Moscow Institute of Physics and Technology |

Known for | Reggeon Field Theory Conformal Field Theory Migdal-Polyakov Bootstrap Migdal-Kadanoff Recursion Loop Equations Matrix Models |

Awards | Landau-Weizmann Award (1996) |

Scientific career | |

Fields | Theoretical High Energy Physics Laser scanning Stock market prediction |

Institutions | Princeton University Landau Institute for Theoretical Physics (ITP) |

## Contents

## Scientific careerEdit

Alexander Migdal made important contributions to the theory of critical phenomena, quantum chromodynamics and conformal field theory. As an undergraduate student he worked out (with Alexander Polyakov) the theory of the dynamical mass generation in gauge theories, commonly
referred to as the "Higgs mechanism",^{[1]}^{[2]} in the spring of 1965,^{[3]}
independently
^{[3]}^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}
of Robert Brout, François Englert and Peter Higgs.^{[9]}

In 1968 he published a paper (with Vladimir Gribov) which introduced (in the context of the Reggeon field theory) scale invariance with anomalous dimensions to be determined as eigenvalues of bootstrap equations of quantum field theory.^{[10]} This work led to so called Migdal-Polyakov conformal bootstrap^{[11]}^{[12]} which had profound influence and helped to make progress in the theory of critical phenomena as well as the theory of strong interactions.^{[13]}

In the next decade Migdal made important progress in quantum chromodynamics by introducing a novel form of the renormalization group (now called Migdal-Kadanoff renormalization),^{[14]}^{[15]} and by deriving (with Yu. Makeenko) the equation for the Wilson loops.^{[16]}^{[17]} The so-called Migdal program^{[18]}^{[19]} was a precursor and provided an impetus to the Shifman-Vainshtein-Zakharov sum rule method (SVZ sum rules) in QCD^{[20]}
which presently plays a basic role in the calculations of hadronic properties. Later he found exact solution of quantum gravity in two dimensions (with V. Kazakov and D. Gross), starting the topic of matrix models of topological field theories which occupied the physics community for a number of years.^{[21]}^{[22]}

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.^{[23]}^{[24]} He initiated (with V. Gurarie, G. Falkovich, and V. Lebedev) a description of intermittency in nonlinear systems by means of Instanton solutions of the stochastic differential equations.^{[25]}

## EntrepreneurshipEdit

Leaving Princeton tenure in 1996, he became an inventor and entrepreneur. He holds 10+ patents in laser scanning and 3D data compression/transmission,^{[26]} built (with A. Lebedev and M. Petrov) first textured 3D scanner which was awarded as Best Of What's New and other industrial awards.^{[27]} 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.

## Selected Books, Poems, and EssaysEdit

- A. A. Migdal, "Loop Equations and 1/N Expansion"
- A. A. Migdal, "English Prose"
- A. A. Migdal, "Russian Prose"
- A. A. Migdal, "Russian Poems"

## External linksEdit

## ReferencesEdit

**^**A. A. Migdal and A. M. Polyakov, "Spontaneous Breakdown of Strong Interaction Symmetry and Absence of Massless Particles",*Soviet Physics JETP*, July 1966**^**"Princeton celebrates Polyakov's 60th".*Cern Courier*. Archived from the original on 2011-07-09. Retrieved 27 May 2013.- ^
^{a}^{b}A.M. Polyakov, A View From The Island, 1992 **^**Farhi, E., & Jackiw, R. W. (1982).*Dynamical Gauge Symmetry Breaking: A Collection Of Reprints*. Singapore: World Scientific Pub. Co.**^**Close, Frank. "The Infinity Puzzle." 2011, p.158**^**The Guardian, Norman Dombey, "Higgs Boson: Credit Where It's Due", July 6, 2012 [1]**^**"Cern Courier, Mar 1, 2006". Archived from the original on 2011-07-09. Retrieved 2013-05-05.**^**Carrol, Sean,"The Particle At The End Of The Universe: The Hunt For The Higgs And The

Discovery Of A New World", 2012, p.228 [2]**^**See footnote No. 1 in Steven Weinberg "The Crisis of Big Science", New York Review of Books, May 10, 2012**^**V. N. Gribov and A. A. Migdal, "Strong Coupling in the Pomeranchuk Pole Problem",*Soviet Physics JETP*, October 1968**^**A. M. Polyakov, "Conformal Symmetry Of Critical Fluctuations", Journal of Experimental and Theoretical Physics Letters, Vol. 12, 1970.**^**A. A. Migdal, "Conformal Invariance and Bootstrap",*Physics Letters B*, December 1971**^**K.G. Wilson, Nobel Lecture, 1982**^**A. A. Migdal, "Phase Transitions in Gauge and Spin Lattice Systems",*Soviet Physics JETP*, October 1975**^**Leo P. Kadanoff, "Notes on Migdal's Recursion Formulas",*Annals of Physics*, September 1976**^**Yu. M. Makeenko and A. A. Migdal, "Exact Equation for the Loop Average in Multicolor QCD",*Physics Letters B*, December 1979**^**A. A. Migdal, "Hidden Symmetries of Large N QCD",*arXiv*, October 1996**^**A. A. Migdal, "Series Expansion for Mesonic Masses in Multicolor QCD",*Annals of Physics*, January 1978**^**Alexander Migdal, "Meromorphization of Large N QFT",*arXiv*, October 2011**^***Vacuum Structure and QCD Sum Rules*, Ed. M. Shifman (North-Holland, 1992)**^**V. A. Kazakov and A. A. Migdal, "Recent Progress in the Theory of Noncritical Strings",*Nuclear Physics B*, December 1988**^**David J. Gross and A. A. Migdal, "A Nonperturbative Treatment of Two-Dimensional Quantum Gravity", Nuclear Physics B, August 1990**^**A. A. Migdal, "Loop Equation and Area Law in Turbulence", 'arXiv*, October 1993***^**A. A. Migdal, "Turbulence as Statistics of Vortex Cells",*arXiv*, June 1993**^**G. Falkovich, I. Kolokolov, V. Lebedev, and A. Migdal "Instantons and Intermittency",*Physical Review E*, November 1996**^**A. Lebedev, A. A. Migdal, and M. Petrov, "System and Method for Rapid Shaped Digitizing and Adaptive Mesh Generation", November 1999**^**"Spinning a 3-D Web",*Popular Science*, December 1999