





Top
results: 1) Gauge gravitation theory on natural bundles
where gravity is a classical Higgs field providing a world manifold
with a Lorentz structure. 2) Comprehensive geometric
formulation of classical field theory where classical fields are
represented by sections of fibre bundles, including: (i)
the differential calculus on graded fibred manifolds and
cohomology of a variational bicomplex, (ii) Lagrangian formalism
on fibre bundles and graded manifolds in terms of infiniteorder
jets, (iii) generalized Noether theorems for reducible degenerate
Lagrangian systems in homology terms, (iv) prequantum BRSTextended
Lagrangian theory of fields, higherorder antifields and ghosts.
3) Covariant Hamiltonian field theory on
polysymplectic manifolds. 4) Classical
Higgs field theory on composite bundles.
5) Geometric formulation of nonrelativistic timedependent mechanics
in terms of fibre bundles over R. 6) Its quantization in a form
of geometric quantization of symplectic foliations. 7) Geometric
formulation of relativistic mechanics in terms of jets of onedimensional
submanifolds. 8) Extension of the LiouvilleArnold, Nekhoroshev
and MishchenkoFomenko theorems on integrable Hamiltonian systems
to a general case of not necessary compact invariant submanifolds.
Brief exposition

Total
publication list



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Gravitation
Gauge Theory at

Beig
a pseudoRiemannian metric from the mathematical viewpoint, gravity
by its
physical nature
is a classical Higgs field. A conjecture is that, being a Higgs
field, a metric gravitational field is not quantized, but it is
classical in principle.

Course
of Theoretical Physics: TheorminimumXXI

This
Course is alternative to the wellknown Course of Theoretical Physics
by Lev Landau in the middle of XX century. Its five volumes provide
contemporary geometric and algebraic topological methods in field
theory, quantum theory, and mechanics.


