The semantics of the canonical commutation relation

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.

References in corpus (1)

• A Topos Foundation for Theories of Physics: I. Formal Languages for Physics

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