Heisenberg group Heisenberg group In mathematics, the Heisenberg group formula_1, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form under the operation of matrix multiplication. Elements "a, b" and "c" can be taken from any commutative ring with identity, often taken to be the ring of real numbers (resulting in the "continuous Heisenberg group") or the ring of integers (resulting in the "discrete Heisenberg group"). The continuous Heisenberg group arises in the description of one-dimensional quantum mechanical systems, especially in the context of the Stone–von Neumann theorem. More generally, one can consider Heisenberg groups associated to
Werner Heisenberg president of the "Alexander von Humboldt-Stiftung" by Konrad Adenauer. Heisenberg served until 1975. Also, from 1953, Heisenberg's theoretical work concentrated on the unified field theory of elementary particles. In 1958 the Max-Planck-Institut für Physik was moved to Munich, expanded, and renamed Max-Planck-Institut für Physik und Astrophysik (MPIFA). In the interim, Heisenberg and the astrophysicist Ludwig Biermann were co-directors of MPIFA. Heisenberg also became an "ordentlicher Professor" (ordinarius professor) at the Ludwig-Maximilians-Universität München. Heisenberg was the sole director of MPIFA from 1960 to 1970. Heisenberg resigned his directorship of the MPIFA on 31 December 1970. In 1946 the German scientist Heinz