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
Martin Heisenberg genetic foundations of the Drosophila brain by studying the effect of genetic mutations on brain function. In addition, Heisenberg contributed a number of essays on the topics of science in society, perception, as well as the question of the freedom of the will. He was elected as a member of the Leopoldina in 1989. Martin Heisenberg is a son of the physicist Werner Heisenberg, who is known for the uncertainty principle. He is married to Apollonia, Countess of Eulenburg. They have four sons, including film director Benjamin Heisenberg. He is the brother of physicist Jochen Heisenberg. Martin Heisenberg Martin Heisenberg