

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 Smatrix, 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 threedimensional metrics rather than in
Minkowski spacetime. 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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