Poisson bracket relations for relativity groups

Details Poisson bracket relations for relativity groups Poisson bracket relations for relativity groups

2008-10-25

arxiv.org/abs/0810.4637v3

Physics

Classical Physics

26 pages

Scientific paper

Poisson bracket relations for generators of canonical transformations are derived directly from the Galilei and Poincare 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 Poincare group. 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.

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