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 bracket. This Lie algebra is a one-dimensional central extension of the commutative Lie algebra formula_57, isomorphic to the Lie algebra of the Heisenberg group. The general abstraction of a Heisenberg group is constructed from any symplectic vector space. For example, let ("V",ω) be a finite-dimensional real symplectic vector space (so ω is a nondegenerate skew symmetric bilinear form on "V"). The Heisenberg group H("V") on ("V",ω) (or simply "V" for brevity) is the set "V"×R endowed with the group law The Heisenberg group is a central extension of the additive group "V". Thus there is an exact sequence Any symplectic