The semantics of the canonical commutation relation
Mathematical Physics
2016-04-27 v1 math.MP
Abstract
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.
Cite
@article{arxiv.1604.07745,
title = {The semantics of the canonical commutation relation},
author = {Boris Zilber},
journal= {arXiv preprint arXiv:1604.07745},
year = {2016}
}