

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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