English

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.

Keywords

Cite

@article{arxiv.1604.07745,
  title  = {The semantics of the canonical commutation relation},
  author = {Boris Zilber},
  journal= {arXiv preprint arXiv:1604.07745},
  year   = {2016}
}
R2 v1 2026-06-22T13:41:26.218Z