Heisenberg group by 90°. The other reflections are "xyx" and "yxy", and rotation by 180° is "xyxy" (="yxyx"). The Lie algebra formula_16 of the Heisenberg group formula_1 (over the real numbers) is the space of formula_18 matrices of the form with formula_20. The following three elements form a basis for formula_16: The basis elements satisfy the commutation relations: The name "Heisenberg group" is motivated by the preceding relations, which have the same form as the canonical commutation relations in quantum mechanics: where formula_25 is the position operator, formula_26 is the momentum operator, and formula_27 is Planck's constant. The Heisenberg group formula_1 has
Max Planck Institute for Physics over as managing director. In 1955 the institute made the decision to move to Munich, and soon after began construction of its current building, designed by Sep Ruf. The institute moved into its current location on September 1, 1958 and took on the new name the Max Planck Institute for Physics and Astrophysics, still with Heisenberg as the managing director. In 1991, the institute was split into the Max Planck Institute for Physics, the Max Planck Institute for Astrophysics and the Max Planck Institute for Extraterrestrial Physics. The current directorial board of the institute is Former directors of the institute