Heisenberg group of the Heisenberg group is fairly simple – later generalized by Mackey theory – and was the motivation for its introduction in quantum physics, as discussed below. For each nonzero real number formula_27, we can define an irreducible unitary representation formula_48 of formula_31 acting on the Hilbert space formula_50 by the formula: This representation is known as the Schrödinger representation. The motivation for the this representation is the action of the exponentiated position and momentum operators in quantum mechanics. The parameter formula_52 describes translations in position space, the parameter formula_53 describes translations in momentum space, and the parameter formula_54 gives
Werner Heisenberg shortly after World War II, Heisenberg briefly returned to the subject of his doctoral thesis, turbulence. Three papers were published in 1948 and one in 1950. In the post-war period Heisenberg continued his interests in cosmic-ray showers with considerations on multiple production of mesons. He published three papers in 1949, two in 1952, and one in 1955. In late 1955 to early 1956, Heisenberg gave the Gifford Lectures at St Andrews University, in Scotland, on the intellectual history of physics. The lectures were later published as "Physics and Philosophy: The Revolution in Modern Science". During 1956 and 1957, Heisenberg was