Based on the assumption that mechanical systems can be described by Lagrangians and time progresses in a fixed direction, a dynamical C*-algebra is presented for nonrelativistic particles at atomic scales.
This algebra is based on the concept of operations and relies exclusively on classical concepts. Nevertheless, it is inherently non-commutative. Without presupposing any quantization scheme, the Heisenberg
commutation relations for position and velocity measurements are derived from it. Hilbert space representations of the algebra lead to the conventional framework of quantum mechanics, providing a new look on its foundations.
(Joint work with Klaus Fredenhagen).