Hidden invariance of the free classical particle
arXiv:hep-th/9306040 · doi:10.1119/1.17514
Abstract
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 is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under 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.
arXiv comment<[email protected]>, LaTeX, 26 pages, some stylistic corrections, enlarged bibliography