Curvature forms and interaction of fields. (English) Zbl 1235.58029

Summary: We work out the general idea that a composite continuous physical system can be mathematically modelled locally as a completely integrable geometric distribution on a manifold, the time-recognizable subsystems to be modelled by corresponding subdistributions, and any local interaction between two subsystems of the physical system to be described in terms of the nonintegrability of the two subdistributions making use of the corresponding two curvature forms. As an illustration we present the corresponding description of photon-like objects, based on the notion that photon-like objects are real, massless time-stable physical objects with intrinsically compatible translational-rotational dynamical structure. The spatial propagation of the system follows some external/shuffling symmetry of the distribution.


58Z05 Applications of global analysis to the sciences
58A30 Vector distributions (subbundles of the tangent bundles)
78A99 General topics in optics and electromagnetic theory
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests