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 Max Planck Institute for Physics The Max Planck Institute for Physics (MPP) is a physics institute in Munich, Germany that specializes in high energy physics and astroparticle physics. It is part of the Max-Planck-Gesellschaft and is also known as the Werner Heisenberg Institute, after its first director in its current location. The founding of the institute traces back to 1914, as an idea from Fritz Haber, Walther Nernst, Max Planck, Emil Warburg, Heinrich Rubens. On October 1, 1917, the institute was officially founded in Berlin as "Kaiser-Wilhelm-Institut für Physik" (KWIP, Kaiser Wilhelm Institute for Physics) with Albert Einstein as the