Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bracket relations for relativity groups   Poisson bracket relations for generators of canonical transformations are
derived directly from the Galilei and Poincar\'e groups of changes of
space-time coordinates. The method is simple but rigorous. The meaning of each
step is clear because it corresponds to an operation in the group of changes of
space-time coordinates. Only products and inverses are used; differences are
not used. It is made explicitly clear why constants occur in some bracket
relations but not in others, and how some constants can be removed, so that in
the end there is a constant in the bracket relations for the Galilei group but
not for the Poincar\'e group. Each change of coordinates needs to be only to
first order, so matrices are not needed for rotations or Lorentz
transformations; simple three-vector descriptions are enough.
  Conversion to quantum mechanics is immediate. One result is a simpler
derivation of the commutation relations for angular momentum directly from
rotations. Problems are included.

5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn