1993/06/30 by Santiago Molina García, Santiago García
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Data Management and Algorithms #Equations of motion #Free particle #Galileo (satellite navigation) #Geometry #Global symmetry #Group (periodic table) #Homogeneous space #Lagrangian #Mathematical physics #Mathematics #Mechanics #Noether's theorem #Physics #Quantum #Quantum mechanics #Rotational symmetry #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #Symmetry group #Symmetry operation #Theoretical physics #Topological and Geometric Data Analysis #advanced mathematical theories #hep-th
paper · pdf · doi:10.1119/1.17514
<[email protected]>, LaTeX, 26 pages, some stylistic corrections, enlarged bibliography
arxiv created 1994/03/12 · openalex publication_date 1994/06/01 · arxiv updated 2016/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group G is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under G leads to a larger symmetry group, which is a central extension of the Galileo group by the real numbers. We study the dynamics associated with this group, and characterize quantities like Noether invariants and evolution equations in terms of group geometric objects. An extension of the Galileo group by U(1) leads to quantum mechanics.