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Mathematical methods in quantum field theory,
axiomatic and constructive QFT, geometry of gauge fields and constrained
dynamics, nonlocal field models.
Main results
include a comprehensive comparative study of the topological
obstructions to global gauge fixing in Yang-Mills theory and
string theory, a new method for establishing the PCT and spin-statistics
theorems which covers nonlocal fields, the derivation of the strong
cluster decomposition properties for field theories with arbitrary
high-energy behavior, the development of a general distribution - theoretic
formalism for covariant quantization of gauge theories.
The current research interests
cover nonperturbative methods in QFT and quantum field models with singular
infrared or/and utraviolet behavior.
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