Physics of Scale Activities

Alexander Polyakov


Russian Physicist. Polyakov studied physics at the Moscow Physical Technical Institute, under Professor Arkadii Migdal. Working with Migdal’s son, Alexander Migdal, Polyakov demonstrated that within gauge invariant field theories having massless particles, the symmetry can be spontaneously broken by what is now called the Higgs mechanism. By using the S-matrix, they showed that in such a gauge theory with a spontaneously broken symmetry the gauge bosons become massive and there are no mass zero particles. Polyakov’s approach was unusual in that he worked in quantum field theory and condensed matter physics simultaneously. He was thus an early advocate of using field theory for describing phase transitions. Alongside Migdal, Polyakov took the work of Valery Pokrovsky and Alexander Patashinski of 1964 and reformulated it in terms of dispersion relations in particle physics. Polyakov demonstrated the consistency of relativistic field theories with anomalous dimensions, by introducing an operator product expansion. That work was like the independent works of Leo P. Kadanoff and Kenneth G. Wilson. But Polyakov focused on electron positron annihilation and deep inelastic scattering. Having noticed a conformal symmetry in critical phenomena, Polyakov then began trying to classify fixed points using possible operator product expansions, even for three dimensions, to calculate critical exponents. But then Wilson’s definitive work on the 4 minus epsilon expansion appeared, providing a way to do calculations. Still, Polyakov prominently showed that some important results can be obtained in three-dimensional metrics rather than in Minkowski space-time. His contributions found many applications in statistical physics and in condensed matter physics.

Alexander Polyakov is a Professor of Physics at Princeton University.

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