2013/06/30 by Gianluca Calcagni · 1 citation
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Geometry #Homogeneous space #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Spacetime #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.88.065005
published as Phys. Rev. D 88, 065005 (2013) · 7 pages. v2: minor typos corrected
openalex publication_date 2013/09/03 · arxiv created 2013/09/04 · arxiv updated 2013/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the action and the dynamics of a relativistic particle, uncharged or charged, in multiscale spacetimes. Invariance under reparametrizations and Poincar'e symmetries uniquely determine the action and the line element to be the usual ones, without the weight factors typical of particle mechanics in these geometries. The resulting spacetime is multiscale only along spatial directions. This version of the system is also dictated by recovery of the nonrelativistic limit together with compatibility with Maxwell and electrodynamics field theory. Giving up all these requirements and allowing for a nontrivial weight factor in the time direction produces a modified line element and considerably complicates the dynamics in the case of a charged particle.