The paper contains presentation of the finite-dimensional approach to the classical field theory based on the geometry of differential manifolds and forms. Geometrical construction of a symplectic structure and Poisson brackets on the space of initial conditions are realized. This space is not a manifold but it can be furnished with a structure of a differential space. The structural n+1 form for the Yang-Mills field theory is constructed. This gives automatically equations of motion and equations for initial conditions. The parasymplectic structure is computed. The directions of degeneration appear to be exactly the directions of infinitesimal gauge transformations. The Poisson bracket for Yang-Mills field theory is obtained.
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- 1 - Physical Sciences ; 2 - Mathematics ; 3 - Mathematical Physics
- 1 - Physical Sciences ; 2 - Physics and Astronomy ; 3 - Statistical and Nonlinear Physics