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Elementary particle physics, foundations
of quantum field theory, renormalization theory,
gauge theories of general type, constrained dynamics.
The main results:
particular solutions to renormalization group
equations and asymptotical free models of massive fields, a
consistent approach to the gauge theory renormalization based on
understanding it as a problem of continuous deformation of the
quantum action and the initial gauge symmetry.
Presently
the investigations are focussed on applications of the theory of
selfadjoint extensions of Hermitian operators to integrable
dynamical systems.
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