I have a problem with the derivation of the the form of QM starting from the Lie algebra of the Galilei Group like the one given in Ballentine's cap 3.(adsbygoogle = window.adsbygoogle || []).push({});

My Issue is that the procedure is shown almost as unavoidable, And my feeling is that there have to be more postulates that I'm not seeing because they are not stated explicitly.

For example, the operator of translation is identified with the Momentum, and in that way they show the quantum commutation relations. I basically understand the Math of the generators of the Galilei group, But that procedure can't be unique because there is another theory in which the momentum operator is not identified with the translation operator and commute with the position operator, namely classical mechanics

http://arxiv.org/abs/1105.4014

So, what is really happening?

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# Galilei Algebra and QM

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