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Preprint Number 1044

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1044. Boris Zilber
The semantics of the canonical commutation relation

Submission date: 26 April 2016


We treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics and establish a geometric semantics of this syntax.
This leads us to a geometric model, the space of states with the action of time evolution operators, which is a limit of finite models. The finitary nature of the space allows to give a precise meaning and calculate various classical quantum mechanical quantities.

Mathematics Subject Classification: 81S05, 03C60

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Full text arXiv 1604.07745: pdf, ps.

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