Hidden invariance of the free classical particle

Details Hidden invariance of the free classical particle Hidden invariance of the free classical particle

1993-06-07

arxiv.org/abs/hep-th/9306040v3

Physics

High Energy Physics

High Energy Physics - Theory

<garcia@het.brown.edu>, LaTeX, 26 pages, some stylistic corrections, enlarged bibliography

Scientific paper

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.

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