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
Werner Heisenberg was established by the "Max-Planck Gesellschaft" (MPG, Max Planck Society, successor organization to the "Kaiser-Wilhelm Gesellschaft"). Heisenberg was appointed president of the "Deutsche Forschungsrat". In 1951, the organization was fused with the Notgemeinschaft der Deutschen Wissenschaft (NG, Emergency Association of German Science) and that same year renamed the "Deutsche Forschungsgemeinschaft" (DFG, German Research Foundation). With the merger, Heisenberg was appointed to the presidium. In 1952, Heisenberg served as the chairman of the Commission for Atomic Physics of the DFG. Also that year, he headed the German delegation to the European Council for Nuclear Research (CERN). In 1953, Heisenberg was appointed