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

Bayak, Igor V.

J. Geom. Symmetry Phys. 38, 1-23 (2015).

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.

MSC:

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

Keywords:

vector fields; algebra of linear vector fields; dynamic flow; topological features