Theoretical and mathematical physicist Moscow State University, Lepage Research Institute400+ scientific publications including 28 books 110+ works reviewed in Mathematical Reviews 2450+non-self citations including 280+ in WikipediA


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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 infinite-order jets, (iii) generalized Noether theorems for reducible degenerate Lagrangian systems in homology terms, (iv) prequantum BRST-extended Lagrangian theory of fields, higher-order antifields and ghosts. 3) Covariant Hamiltonian field theory on polysymplectic manifolds. 4) Classical Higgs field theory on composite bundles. 5) Geometric formulation of non-relativistic time-dependent 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 one-dimensional submanifolds. 8) Extension of the Liouville-Arnold, Nekhoroshev and Mishchenko-Fomenko theorems on integrable Hamiltonian systems to a general case of not necessary compact invariant submanifolds. Brief exposition

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Gravitation Gauge Theory at Sardanashvily on Facebook

Beig a pseudo-Riemannian 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: Theorminimum-XXI in Russian Sardanashvily on Facebook

This Course is alternative to the well-known 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.