2014/04/11 by Manouchehr Amiri, Amiri, Manouchehr
Physics and Astronomy · #Astro and Planetary Science #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1405.2052
openalex publication_date 2014/04/11 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28
We introduce a type of symmetry breaking and associated order parameter in\nconnection with Laplace-Runge-Lenz vector of Kepler orbit through an extended\nspatial dimension and Ensemble view. By implementation of a small extra spatial\ndimension and embedded infinitesimal toral manifold, it has been shown that\nemerging of LRL vector under SO(4)symmetry is in analogy with a variety of\nexplicit and spontaneous symmetry breaking situations and related Goldstone\nbosons such as phonons and spin waves. A theorem introduced to generalize this\nconcept of breaking symmetry. The diffeomorphism of circular orbit(geodesic)to\nelliptic one proved to be equivalent with a covariant derivative and related\nparallel displacement in this extended four dimensional spatial space.Respect\nto ensemble definition this diffeomorphism breaks the O(2) symmetry of initial\norbit and Hamiltonian to Z2 resulting in broken generators in quotient space\nand associated Goldstone boson as perturbing Hamiltonian term leading to a\nperpetual circular motion on 2-torus comparable to the perpetual motion idea in\nTime Crystal of Wilczek. This leads to an introduction of gravitational gauge\npotential under the symmetry of Cartan sub algebra of su(2).\n