Heisenberg cut Heisenberg cut In quantum mechanics, a Heisenberg cut is the hypothetical interface between quantum events and an observer's information, knowledge, or conscious awareness. Below the cut everything is governed by the wave function; above the cut a classical description is used. The Heisenberg cut is a theoretical construct; it is not known whether actual Heisenberg cuts exist, where they might be found, or how they could be detected experimentally. However, the concept is useful for analysis. The cut is named after Werner Heisenberg's work on the Copenhagen interpretation of quantum mechanics in which it is associated with wave function collapse.
Heisenberg group case is the theta representation of the Heisenberg group, of which the discrete case gives the theta function. The Heisenberg group also occurs in Fourier analysis, where it is used in some formulations of the Stone–von Neumann theorem. In this case, the Heisenberg group can be understood to act on the space of square integrable functions; the result is a representation of the Heisenberg groups sometimes called the Weyl representation. The three-dimensional Heisenberg group "H"(R) on the reals can also be understood to be a smooth manifold, and specifically, a simple example of a sub-Riemannian manifold. Given a point "p"=("x","y","z")