Applications of the local algebras of vector fields to the modelling of physical phenomena. (English) Zbl 1348.53015

Summary: We discuss the local algebras of linear vector fields that can be used in the mathematical modelling of physical space by building the dynamical flows of vector fields on eight-dimensional cylindrical or toroidal manifolds. It is shown that the topological features of the vector fields obey the Dirac equation when moving freely within the surface of a pseudo-sphere in the eight-dimensional pseudo-Euclidean space.


53A45 Differential geometric aspects in vector and tensor analysis
53Z05 Applications of differential geometry to physics
37C10 Dynamics induced by flows and semiflows
53B50 Applications of local differential geometry to the sciences
57R25 Vector fields, frame fields in differential topology
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
15A66 Clifford algebras, spinors