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 the special property that the exponential map is a one-to-one and onto map from the Lie algebra formula_16 to the group formula_1. More general Heisenberg groups formula_31 may be defined for higher dimensions in Euclidean space, and more generally on symplectic vector spaces. The simplest general case is the real Heisenberg group of dimension formula_32, for any integer formula_33. As a group of matrices, formula_31 (or formula_35 to indicate this is the Heisenberg group over the field formula_36 of real numbers) is defined as the group formula_37 matrices with entries in formula_36 and having the form: where This is indeed