2004/09/30 by A. N. Grigorenko
Mathematics · Physics and Astronomy · #Action (physics) #Algebraic and Geometric Analysis #Canonical coordinates #Classical mechanics #Eigenvalues and eigenvectors #Geodesic #Geometry #Lorentz transformation #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Phase space #Physics #Quantum mechanics #Relativity and Gravitational Theory #Scalar (mathematics) #Scaling #Vector field #physics.class-ph #physics.gen-ph
paper · pdf · doi:10.1016/j.geomphys.2014.07.022
published as Journal of Geometry and Physics, vol. 86, 94-100, 2014 · 25 pages
arxiv created 2014/04/16 · openalex publication_date 2014/07/19 · openalex created_date 2016/06/24 · arxiv updated 2019/01/31 · openalex updated_date 2026/08/05
We formulate geodesics on a manifold in terms of a parallel transfer of a particle state vector transformed by local Lorentz and Yang-Mills symmetry groups. This formulation leads to an introduction of a canonical one-form the eigenvalues of which define distance on a manifold. We suggest an action based on the canonical distance form and apply it to describe classical particles with spin. Arguments are presented in favour of scaling distance in the space-time with a scalar field.