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
Benjamin Heisenberg Benjamin Heisenberg Benjamin Heisenberg (born 9 June 1974) is a German film director and screenwriter. He has directed sixteen films since 1995. His film "Schläfer" was screened in the Un Certain Regard section at the 2005 Cannes Film Festival. His 2010 film, "The Robber", was nominated for the Golden Bear at the 60th Berlin International Film Festival. He is also the grandson of Nobel Prize winning physicist Werner Heisenberg via father Martin Heisenberg. He is co-editor and co-publisher of the German film magazine Revolver. Benjamin Heisenberg was born in Tübingen, Germany to Martin Heisenberg and Apollonia, Countess of Eulenburg. He