SPACE, TIME AND FUNDAMENTAL INTERACTIONS

ON THE USE OF BIVECTOR FORMALIZM IN HAMILTONIAN MECHANICS

Morozov E. A., Morozova A.R., Morozova L.E

A bivector formalism of Hamiltonian mechanics is constructed. The extended affine space of impulses, coordinates, and time is determined based on the determinism principle. The space attached to it is considered as a direct sum of the covariant space of pulses and the contravariant space of coordinates and time, after which the bivector space of pulses, coordinates and time is determined. The resulting point-bivector correspondence allows us to determine the corresponding extended phase space and flow. It turns out that the bivector analog of the dynamic Hamilton equations has the form of the dynamic Newton equation for the potential field. We consider a bivector variant of canonical transformations that define the geometry of a bivector phase space. The use of covariant and contravariant vector spaces, as well as basic tensor operations, makes it possible to significantly simplify the transformation algebra in proofs.