Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hidden invariance of the free classical particle   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.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an