Quantization and renormalization of gauge theories,
geometrical and deformation quantization, dynamics and quantization
of relativistic particle models
The main results:
quantum mechanical problem of the electron moving in the AharonovBom
potential is formulated and solved as a problem of constructing the
selfadjoint extension of the Hamiltonian; discovery of the global (BRST)
supersymmetry of the effective action of quantum gauge theory; proof of gauge
invariant renormalizability of a general gauge theory и independence of the
betafunctions from gauge fixing (with B.Voronov); proof of the equivalence
of the Lagrange and Hamilton quantizations of gauge theories (with I.Batalin
and R.Grigoryan; a method of constructing the asimptotically free models is
developed (with B.Voronov); the Sp(2)covariant formulation of general gauge
theory (with I.Batalin, P.Lavrov) and general covariant fieldantifield
formalism (with I.Batalin) are constructed; mathematical correct formalism in
which the action of higher order variational local differential operators on
local functionals does not contain indefinite quantities like delta(0) is
developed (with B.Voronov and S.Shahverdiev); general forms of the *products
and *commutators on the Grassman algebra are found.
Two monographies on quantization of the constraint systems:
D.M.Gitman, I.V.Tyutin. Canonical quantization of Fields with
Constraints (in Russian), Наука, Москва, 1986, 216 p.;
D.M.Gitman, I.V.Tyutin. Quantization of Fields with Constraints,
SpringerVerlag, 1990, 291 p.
The current interests:
dual models, relativistic particle models, general
covariant formulation of gauge theories in the fieldantifield formalism,
некоммутативное произведение.
