Year: 2001
Type: article
Abstract: The maximal invariance group of Newton’s equations for a free nonrelativistic point particle is shown to be larger than the Galilei group. It is a semidirect product of the static (nine-parameter) Galilei group and an SL(2,R) group containing time translations, dilations, and a one-parameter group of time-dependent scalings called expansions. This group was first discovered by Niederer in the context of the free Schrödinger equation. We also provide a road map from the free nonrelativistic point particle to the equations of fluid mechanics to which the symmetry carries over. The hitherto unnoticed SL(2,R) part of the symmetry group for fluid mechanics gives a theoretical explanation for an observed similarity between numerical simulations of supernova explosions and numerical simulations of experiments involving laser-induced implosions in inertial confinement plasmas. We also give examples of interacting many-body systems of point particles which have this symmetry group.
Source: American Journal of Physics
DOI: 10.1119/1.1379736
Authors: O. Jahn, V. V. Sreedhar
Institution: Dublin Institute For Advanced Studies
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2033197628