2015/01/01 by Alexander P. Yefremov
Mathematics · Medicine · Physics and Astronomy · #Action (physics) #Advanced Mathematical Theories and Applications #Algebra over a field #Biofield Effects and Biophysics #Classical mechanics #Computer science #Fractal #Geometry #Hypercomplex number #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum Mechanics and Applications #Quantum mechanics #Quaternion #Space (punctuation) #Surface (topology) #physics.gen-ph
paper · pdf · doi:10.1134/s0202289315010144
published as Gravitation and Cosmology, 2015, Vol. 21, No. 1 · 13 pages
openalex publication_date 2015/01/01 · arxiv created 2016/04/29 · arxiv updated 2016/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We trace the logical line of formulating a theory of mechanics founded on the basic relations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical and relativistic mechanics can be regarded as mathematical consequences of a single condition of stability of exceptional algebras of real, complex and quaternion numbers under transformations of primitive constituents of their units and elements. In the course of the study, the notion of a basic fractal surface underlying the physical three-dimensional space is introduced, and an original geometric treatment (admitting visualization) of some formerly considered abstract functions (mechanical action, space-time interval) are suggested.